Upvote:3
Yes, you can enter Brazil with the RNE and your passport.
Timatic, the system which helps airlines verify passenger documents, states:
Visa required, except for Passengers with an ID card issued to residents of Brazil if stay abroad does not exceed 2 years.
Timatic provides a list of valid ID cards, one of which is:
Cedula de Identidade de Estrangerio [sic]
You will notice that your RNE has this phrase printed on it (though spelled correctly).