I have an equation to calculate $A$ from $r$ and $h$: $$ A= \arccos\left(\frac{r-h}{r}\right)r^2 - (r-h)\sqrt{r^2-(r-h)^2} $$
But now $A$ and $r$ are known, and I want to solve for $h$ instead. So far, I solve this equation numerically, but I was wondering whether it can be solved analytically. All three $A$, $r$ and $h$ are positive. I have tried to solve it using Wolfram Alpha, but I only get a timeout. Any better ideas?