MathNet 2016-part-06 — 184 problems (EN–VI) Question 70

Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that for all $x, y \in \mathbb{R}$:
$$
(f(x)+y)(f(x-y)+1)=f(f(x f(x+1))-y f(y-1))
$$