Amarande: 11 Nd4+ might perhaps be best, returning the piece; Tartakower, to my recollection, commented on this possibility as giving (along the lines of - I don't have the book in front of me) "a defensive tempo of no small importance."
After this, the natural continuation would be 11 ... b5 12 Be3 bxa4 13 Nf3 Qh5 14 Nbd2 (to eliminate the Ne4) after which Black appears to win with 14 ... O-O. White must chase his material, being two pawns down and Black's King has just gotten into safety, so 15 Nxe4 dxe4 16 Nxh2 Qxh2 17 Bc5 Re8 18 Qd5 Rb8 19 Qc6 is indicated, causing some trouble as Black's pawns are weak, but Black still seems to have it in the bag after 19 ... Qh1+ 20 Ke2 Bg4+ 21 Kd2 (21 f3 exf3+ looks even more dangerous) Rbd8+ 22 Kc3 Qxg2 23 Qxa6 Ra8 24 Qc6 Rec8! This last saves the most important pawn, preventing White from having a passed pawn to balance the h-pawn.
Black is then still two pawns up, and White can only regain one by submitting to an exchange of Queens, either by 25 Qxe4 etc. or with 25 Rxe4 Qf3+ (Black must be a little wary - if at once 25 ... Bf5?? 26 Re8+! is sorrow) 26 Be3 Bf5, forcing 27 Rc4. In addition, he has a strong K-side majority and a passed h-pawn, with the right Bishop to boot.
I see no reason White should be able to draw this end-game, and, indeed, unless there is some improvement over 14 Nbd2 (there may very well be) find that 10 Kf1 looks to be distinctly inferior.