For a normal distribution, the expectation of the mean and median is the same. However, in finite sample sizes, they will almost always be different. Given a number of observations, they will be more different the higher the standard deviation. Given the standard deviation, they will also be closer the more the observations.
Corrections presents Monte Carlo evidence that allows one to predict the standard deviation from only the absolute difference between mean and median and the number of observations, given the sample was produced using a normal distribution. Given a specific level and the number of observations, one can look up a unique value of the standard deviation.