I am trying to remove the effects from skew from data to find the true mean
Let's say I a priori know that the data is drawn from a true Gaussian distribution, but I am unable to take an infinite (or very very large) sample, and my sample is only $n$ in size. Of this sample of $n$ it will have some mean $\bar{x}$. This will differ ever so slightly from the true mean of $\mu$. I am able to calculate easily the skew $g$ and kurtosis $k$. I will not know the standard deviation of the true distribution (and am not interested in calculating it), but will of course have the standard deviation $\sigma$ of the sample.
As I understand skew, $\bar{x}$ has been shifted slightly due to $g$. I believe some transformation has been applied to the distribution, and would like to try and invert this transformation somehow. The data itself is not important, only finding $\mu$