You can use the inverse erf function, which is available in MatLab and Mathematica, for instance.

For the normal CDF, starting from

$$y=\Phi\left(x\right)=\frac{1}{2}\left[1+erf\left(\frac{x}{\sqrt{2}}\right)\right]$$

We get

$$x=\sqrt{2}erf^{-1}\left(2y-1\right)$$

For the log-normal CDF, starting from

$$y=F_{x}(x;\mu,\sigma)=\frac{1}{2}erfc\left(\frac{-lnx-\mu}{\sigma\sqrt{2}}\right)$$

We get

$$-\ln\left(x\right)=\mu+\sigma\sqrt{2}erfc^{-1}\left(2y\right)$$

You can use the inverse erf function, 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

$$-\log \left(x\right)=\mu+\sigma\sqrt{2}\ \text{erfc}^{-1}\left(2y\right)$$

Maybe you could use the inverse erf function?

You can use the inverse erf function, which is available in MatLab and Mathematica, for instance.

For the normal CDF, starting from

$$y=\Phi\left(x\right)=\frac{1}{2}\left[1+erf\left(\frac{x}{\sqrt{2}}\right)\right]$$

We get

$$x=\sqrt{2}erf^{-1}\left(2y-1\right)$$

For the log-normal CDF, starting from

$$y=F_{x}(x;\mu,\sigma)=\frac{1}{2}erfc\left(\frac{-lnx-\mu}{\sigma\sqrt{2}}\right)$$

We get

$$-\ln\left(x\right)=\mu+\sigma\sqrt{2}erfc^{-1}\left(2y\right)$$