Since the letter 'e' isn't a word, rules which relate to words tend to break down (or simply not exist).
As an analogy, consider the way that the plurals of abbreviations are written. You will often see sentences written like this one:
There are lots of ISP's
Many editors of magazines and newspapers regard that sentence as correct. They either don't care that the apostrophe doesn't perform one of its normally accepted functions, or they justify its use by stating that it indicates that the term is abbreviated. However, the BBC TV programme 'Never Mind the Full Stops' rejects the apostrophe as unnecessary and regards this as correct:
There are lots of ISPs
So, if 'E' was to be used as an abbreviation (e.g. for an Ectsasy tablet), most editors would opt for this:
He took several E's
However, it seems that the BBC might prefer this:
He took several Es
I've been paid for quite a bit of writing - often with sub-editors replacing correct English with an incorrect version ;-) My preference, for the sentence you cite, would be to adopt the same convention which I've used in the first line of this reply. i.e. to accept that 'e' (there, I've done it again) is being 'quoted'. So your sentence takes this form:
Cheap does not have two 'e's
Chris