ISL 2007 A4

Find all functions $f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$such that $$f(x+f(y))=f(x+y)+f(y)$$ for all $x, y \in \mathbb{R}^{+}$. (Symbol $\mathbb{R}^{+}$denotes the set of all positive real numbers.) (Thaliand)