You can use the [inverse erf function][1], which is available in MatLab and Mathematica, for instance. For the normal CDF, starting from $$y=\Phi\left(x\right)=\frac{1}{2}\left[1+\text{erf}\left(\frac{x}{\sqrt{2}}\right)\right]$$ We get $$x=\sqrt{2}\ \text{erf}^{-1}\left(2y-1\right)$$ For the log-normal CDF, starting from $$y=F_{x}(x;\mu,\sigma)=\frac{1}{2}\text{erfc}\left(\frac{-\log x-\mu}{\sigma\sqrt{2}}\right)$$ We get $$-\log \left(x\right)=\mu+\sigma\sqrt{2}\ \text{erfc}^{-1}\left(2y\right)$$ [1]: http://mathworld.wolfram.com/InverseErf.html