Proving the uniqueness of a solution to $f(x-f(y)) = f(f(y)) + xf(y) + f(x) - 1$
Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.