How to solve the equation $t = \sqrt{x^2 - 1} - x$ for $x$? 
Let the equation $t = \sqrt {x^2 - 1} - x$. Find $x$.

So I've tried the following:
$$t^2 = x^2 - 1 -2\sqrt {x^2-1}x + x^2 = 2x^2 - 2\sqrt{x^2-1}x - 1 $$
What should I do next?

Note that $$\left(\sqrt{x^2-1}-x\right)\left(\sqrt{x^2-1}+x\right) = -1,$$ so $$\frac{1}{t}=-\sqrt{x^2-1}-x$$ Adding we get $$t+\frac{1}{t}=-2x$$ Or:
$$x=\frac{-1}{2}\left(t+\frac{1}{t}\right)$$
