How do Trinitarians explain that Jesus himself claims He is a man who has heard things from God at John 8:40?

Trinitarians believe that Jesus is God and man since the time when Jesus stopped being only immortal and took on flesh. Yet he remained God because God needed to appear to die for the sins of the world.

John 8:40 expresses a moment in time when Jesus is speaking from his flesh - this should not be confused with him being still God at this time because he is in the flesh and this is how he presents himself while on earth. Simultaneously immortal and mortal, knowing and not knowing, supremely powerful but powerless, fully independent but totally dependent. Only his flesh is revealed while his God-ness is hidden (except from Thomas).

Jesus doesn’t ever call himself God or allude to it as he doesn’t want people to be distracted from his ministry in the flesh.

It's not being deceitful or disingenuous to say he is a man when he is really God the whole time. Some say that if Jesus is really God, then this verse makes Jesus a liar - saying he is a man when he is really God. God has light and darkness in His purview (Isaiah 45:7) and can bend the truth to suit His divine purposes.

Peter and the other Apostles don't make a big deal about him being God because they didn’t want to make Jesus complicated while pretending to be just a man the whole time.

Jesus depends on God for all his needs, even though he is always God, as he must show absolute dependency - he could do nothing of himself (so he kept saying anyway) as an example for those watching.

The important thing to remember is; the bible can be confusing. The Creeds provided by the Church Fathers must be honoured first to ensure things are understood correctly. Only then may the bible be in general agreement with the Creedal principles - anything that seems contradictory is set aside as there are some mysteries that are not yet understood.

The trinitarian understanding hinges, in part, on what is meant by morphe in Philippians 2:

Who, being in the form of God, thought it not robbery to be equal with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men,... - Philippians 2:6-7

One cannot simultaneously say that "in the form of God" does not mean he was God but that "in the form of a servant" does mean that he was human. Whatever "in the form" of a servant means so also "in the form" of God must mean.

The only other time this form (pun unavoidable) of morphe is used is Mark 16:12 which says:

After that he appeared in another form unto two of them, as they walked, and went into the country. 

One might be led to believe that Jesus changed his outward appearance by this verse alone however, reading the more detailed account of this incident in Luke 24 reveals that it was the eyes (or perception) of the disciples that were restrained from recognizing Jesus:

And it came to pass, that, while they communed together and reasoned, Jesus himself drew near, and went with them. But their eyes were holden that they should not know him. - Luke 24:15-16

And when they did recognize him, the opening of their eyes is not linked to a change of outward appearance but to a recognizable action or behavior:

And it came to pass, as he sat at meat with them, he took bread, and blessed it, and brake, and gave to them. And their eyes were opened, and they knew him; and he vanished out of their sight. - Luke 24:30-31

By this we can understand the Philippians passage with more specificity. It is not the outward appearance of God and of a servant that is in view (and this makes sense because God, being Spirit, has no outward appearance) but, rather, that perception that is linked to behavior.

With this understanding Philippians 2:6-7 might be rendered something like this: "Even though he had every right to behave and appear as God he abased himself and behaved and appeared as a servant". And this understanding not only makes sense of John 8:40 and so many other passages where Jesus acts and speaks as a man:

But now ye seek to kill me, a man that hath told you the truth, which I have heard of God: this did not Abraham. - John 8:40

But it also makes sense of the times where Jesus implores us that, if we won't believe his words, we should at least believe his works:

Say ye of him, whom the Father hath sanctified, and sent into the world, Thou blasphemest; because I said, I am the Son of God? If I do not the works of my Father, believe me not. But if I do, though ye believe not me, believe the works: that ye may know, and believe, that the Father is in me, and I in him. - John 10:36-38

Believest thou not that I am in the Father, and the Father in me? the words that I speak unto you I speak not of myself: but the Father that dwelleth in me, he doeth the works. Believe me that I am in the Father, and the Father in me: or else believe me for the very works' sake. - John 14:10-11 

These works are the works of his Father. They are the behaviors of God which are meant to affect our perception so that we may see who he is.

Though he rightly had the behavior/nature (in the form) of God, He adopted the behavior/nature (in the form) of a servant and was made in the resemblance (likeness) of a man and, being found in the outward appearance (fashion) of a man he humbled himself, as a man should, and became obedient (to God) as a man should.

He acted and spoke as a man so that we could perceive him as such but he also performed the works of God, humbly (as a servant) saying that it was the Father in Him doing the works, and begging us to believe at the very least because of the works (morphe) of the Father in him.

Why did Jesus so often refer to himself as a man and only vaguely and seldom (according to some) refer to himself as God? It is not so. Seeing they see not and hearing they hear not, neither do they understand as a fulfillment of prophesy:

Therefore speak I to them in parables: because they seeing see not; and hearing they hear not, neither do they understand. And in them is fulfilled the prophecy of Esaias, which saith, By hearing ye shall hear, and shall not understand; and seeing ye shall see, and shall not perceive: For this people's heart is waxed gross, and their ears are dull of hearing, and their eyes they have closed; lest at any time they should see with their eyes, and hear with their ears, and should understand with their heart, and should be converted, and I should heal them. - Matthew 13:13-15

It is not that he did not behave/appear as God (believe because of the works!)... it is that our eyes are holden that we should not know him. It is no accident nor meaningless that opening blind eyes is so prominent in the gospel accounts and is given as a sign of the Christ's coming. Oh, that he may mercifully open the eyes of the blind if we will but cry out and ask:

And they came to Jericho: and as he went out of Jericho with his disciples and a great number of people, blind Bartimaeus, the son of Timaeus, sat by the highway side begging. And when he heard that it was Jesus of Nazareth, he began to cry out, and say, Jesus, thou Son of David, have mercy on me. And many charged him that he should hold his peace: but he cried the more a great deal, Thou Son of David, have mercy on me. And Jesus stood still, and commanded him to be called. And they call the blind man, saying unto him, Be of good comfort, rise; he calleth thee. And he, casting away his garment, rose, and came to Jesus. And Jesus answered and said unto him, What wilt thou that I should do unto thee? The blind man said unto him, Lord, that I might receive my sight. And Jesus said unto him, Go thy way; thy faith hath made thee whole. And immediately he received his sight, and followed Jesus in the way. - Mark 10:46-52

It's a common misapprehension that Trinitarians do not believe the Jesus was a man. However they do believe that. The core of Trinitarian belief is that Jesus is both Man and God.

Also God the Son deliberately and voluntarily made himself dependent on God the Father as part of the incarnation. He chose to be reliant on the Father for his power, his knowledge. So Jesus is absolutely correct to say that he is a man, and to say that he has heard things from God.

While you could theoretically argue that Jesus might have said "I am a man and God", such a statement would not be relevant to the point he was trying to make and would almost certainly have distracted from it.