Need help please: Why did white resign?

... Re8+ followed by ... c4?
Isn't that a piece up?
EDIT: even after Ne4, Black still wins material with ... c4.

After c4, White can move his rook to e3, trade his rook for Black's bishop, and they are even. Why resign?

After c4, White can move his rook to e3, trade his rook for Black's bishop, and they are even. Why resign?
Black checks FIRST at e8 before playing c4.

From a purely amateur point of view you can see early on that white is being pushed around. Black has total control over the board. Black will take more material with c4. Control the e file. White's rooks are all blocked in by his own pawns. It will end up a game where white will struggle to stop the pawn advance without any room to move in.
chessplayer11: I appreciate your analysis very much, especially noting the fact the game was being viewed through an amateur's eyes (mine!). It is all so plain now. I stared at this game for so long. I feel pretty foolish now, because I should have been able to spot the fact that white was going to be bombarded by a pawn onslaught, as well as material loss.
Everyone - thank you so much!!
I was looking over a game (ponziana opening), and I cannot figure out why white resigned. If the answer is obvious, please excuse my ignorance. I am definitely a newbie. Thank you.