Random weibull from mean and variance

I need to sample random values from a Weibull distribution where I know the mean and the variance. I want to use Matlab, whose function wblrnd requires the shape and scale parameters. Now, I have seen from wikipedia that mean and variance are correlated to the shape and scale parameters, but between them there is a Gamma Function. Therefore, I was wondering: is there a way to go analytically from the mean and variance to shape and scale parameters? If not, how could I do that?