Inverse of $f(x)=\sin(x)+x$ What is the inverse of 
$$f(x)=\sin(x)+x.$$
I thought about it for a while but I couldn't figure it out and I couldn't find the answer on the internet.
What about
$$f(x)=\sin(a \cdot x)+x$$
where $a$ is a known real constant.
Thank you for taking the time to read this question!
Sorry if this has been asked before...

Kepler's equation  ... its solution is known not to be an elementary function.
