Except in that example the author is choosing E based on the observed difference between two means (which is the exactly the unknown you're trying to determine, so it makes no sense to use it as a constant in a formula), rather than the threshold for the minimum distance you care about.

If you're going the classical statistics route the entire point is that you need to determine your sample size before you peek at the data. In that post you would need to replace E with a threshold of difference that you care about, then calculate n before you start the test and not look at the results until you had reached n observations.