Determine a method to generate random observations for the extreme valued pdf given by:

$\displaystyle e^{x-e^x} \ \ \ \ \ - \infty < x < \infty$

So I start by finding it's CDF:

$\displaystyle \int^{x}_{-\infty}e^{x-e^x} dx$

and this is where I get stuck. Any help would be appreciated.