No idea how to solve this equation using two exponentials

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The equation I have is:

$$A = B ( \exp(C x) - \exp(-Dx) )$$

How do I solve for $x$ given $A$, $B$, $C$, $D$?

I have no idea how. The only idea I have is that I could express these in terms of a taylor series, but is there a better way that I do not know? I could also generate $A$ based on known $B, C, D$ and for a given range of $x$ of finite steps, then find my particular $A$ of interest and see what $x$ was required. (I'm thinking that's a graphical way to attack this.) But it isn't very satisfying.