Upvote:2
The US has two conflicting rules
In practice #2 trumps #1, so if you manage to get to the border and can prove that you are a US citizen, you will be admitted. They may hassle your for a while, but they will let you in.
The tricky part however is to get on a US bound plane. No airline will let you board unless you have the immigration credentials that the US CBP would like to see. CBP uses the airlines as "enforcer" for rule #1, since they can't enforce it themselves.
You could try an ESTA but chances are it will be denied since you are a US citizen and the ESTA application specifically asks about multiple citizenships. You could lie, but lying to immigration officials in generally a bad idea.
Another option would be to try to get to a land or sea border.