Challenge problem

[navdeep_bajwa]

MGMAT Challenge Problem 12/14/09
If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative integers, what is the greatest possible value of |x - y|?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Please explain it I could not understand the explanation given in MGMAT
Also why cannot the answer be E since greatest value of x can be 4 and least value of y can be 0

[Ben Ku]

Your response would not work. If x = 4 and y = 0, then you have:

2^4 + 2^0 = 4^2 + 0^2
16 + 1 = 16 + 0
17 = 16

This does not work out.