Inverse Function with multiple x terms.

Hi I'm trying to find the inverse function of $\displaystyle f(x) = 8+x^2+tan{\frac{\pi*x}{2}}$ where $\displaystyle -1< x <1$ and $\displaystyle f^{-1}(8)$

The main place i am having trouble is I don't know how to rearrange for x when there is more than 1 x term. The best I've done is; by letting $\displaystyle f(x)= y$, get the equation $\displaystyle y-8=x^2+tan{\frac{\pi*x}{2}}$which doesn't seem to be a great deal better.

Any ideas would be greatly appreciated.