Why does Solve lock up when trying to solve the equation

Solve[(x^2+y^2)+(x+y)==2^511 && x>0 && y>0,{x,y},Integers]

It works up 2^185, but at higher powers of 2, it seems to stop processing. The program says it's running, but there is no solution after running overnight. Running Mathematica 11.3 on Windows 32-bit OS.