Seems begging for contradiction.
Suppose two are rational. Let's take and .
Those can be expressed as ratios of integers.
Solving simultaneously shows e is rational AND is rational, since:
1) Looking at denominators, they must be divisible by 2bd and
2) Looking at numerators, integers are closed over addition, subtraction, and multiplication.
I certainly have not covered the whole proof, but that seems a good piece of it.