No wonder: it is an irrational function and to find roots of such aberrations is a very, very hard task (except in some particular cases). Perhaps some numerical approximation can be tried here... or:

, and squaring both sides and making some order you get the following beast (disclaimer: check this! It can perfectly well be wrong):

. This is a quartic and then it can be solved by the method of Ferrari.

It is going to cost you tears, blood and buckets of sweat to do it without the aid of some program, but it is doable.

If you've the nerve for this, check this Quartic function - Wikipedia, the free encyclopedia ...and may the force and Gauss be with you!

Tonio