One can activate
e only in math mode and only as a math character with mathcode
"8000, that doesn't interfere with macro name scanning:
but I advise against using such an approach. It's better to have a macro
\euler or any other name.
In order to use the special
"8000 mathcode assigned to
e, there must exist a valid definition of
e as active character. Therefore the well-known
\lowercase trick (many commands used there have
e in their names).