Estimate of mean and variance of a Gaussian random variable from its error function

Question

Let's say we have a Gaussian random variable X with mean and variance to be m and s, which are unknown. What can be observed is the error function sampled at a few values of $X=x_i$. Let say $\operatorname{erf}(x_1)=e_1, \operatorname{erf}(x_2)=e_2,\cdots .$ Is there a way to estimate the underlying m and s given $(x_i,e_i)$? Thank you for any suggestions.