BALTIC-WAY 2013 Problem 3

Let $\mathbb{R}$ denote the set of real numbers. Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that

$$f(x f(y)+y)+f(-f(x))=f(y f(x)-y)+y \text { for all } x, y \in \mathbb{R}$$