To determine all the functions $\displaystyle f$ defined on the set of real numbers and obtaining real values such that for any real numbers $\displaystyle x, y$ such equation is true:

$\displaystyle f(x+f(x+y))-f(x-y)-f(x)^2=0$

It works supposing $\displaystyle f(x)=0$ and $f(y)=0$ but I'm clueless on the next step. Could you please help?