I've been wondering about the following for a while:

Function $\displaystyle f: [1, \infty[ \rightarrow R$ is non-negative and implements the equation $\displaystyle x + f(x) = e^{f(x)}$. Find $\displaystyle f(e-1)$ and $\displaystyle f(1)$.

I just cannot get anything out of it.

Do you have any ideas?