We know $e$ and $\pi$ are transcendental. Meaning that they aren't the solutions to any polynomial equation with coefficients that are integers. The next obvious question to ask - what about polynomials with coefficients that are rational numbers? Is there a name for such numbers? And has anyone proven that $e$ and $\pi$ don't belong to this family?
The next obvious extension is polynomials with coefficients that are algebraic numbers.
I assume all of these sets will be countable, so it's almost certain $e$ and $\pi$ won't belong to them. Is this a fair assertion to make?