MathNet 2008-part-04 — 165 problems (EN–VI) Question 78

Let $\mathbb{R}^{+}$ be the set of positive real numbers. Determine all functions $f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ such that for all $x, y \gt 0$
$$
f(x+f(y))=f(x+y)+f(y)
$$