Assuming we are only interested in base 10 and that pi contains e means that at some point in the sequence of decimal digits of pi (3, 1, 4, 1, 5, 9, 2, ...) there is the sequence of decimal digits of e (2, 7, 1, 8, 2, 8, ...), then I believe that question is currently unanswered.
Pi would contain e if and only if there are positive integers n and m such that 10^n pi - m = e, or equivalently 10^n pi - e = m.
We generally don't know if combinations of e and pi of the form a pi + b e where a and b are algebraic are rational or not.
Even the simple pi + e is beyond current mathematics. All we've got there is that at least one of pi + e and pi e must be irrational. We know that because both pi and e are zeros of the polynomial (x-pi)(x-e) = x^2 - (pi+e)x + pi e. If both pi+e and pi e were rational then that polynomial would have rational coefficients, and the roots of a non-zero polynomial with rational coefficients are algebraic (that is in fact the definition of an algebraic number) and both pi and e are known to not be algebraic.
Assuming we are only interested in base 10 and that pi contains e means that at some point in the sequence of decimal digits of pi (3, 1, 4, 1, 5, 9, 2, ...) there is the sequence of decimal digits of e (2, 7, 1, 8, 2, 8, ...), then I believe that question is currently unanswered.
Pi would contain e if and only if there are positive integers n and m such that 10^n pi - m = e, or equivalently 10^n pi - e = m.
We generally don't know if combinations of e and pi of the form a pi + b e where a and b are algebraic are rational or not.
Even the simple pi + e is beyond current mathematics. All we've got there is that at least one of pi + e and pi e must be irrational. We know that because both pi and e are zeros of the polynomial (x-pi)(x-e) = x^2 - (pi+e)x + pi e. If both pi+e and pi e were rational then that polynomial would have rational coefficients, and the roots of a non-zero polynomial with rational coefficients are algebraic (that is in fact the definition of an algebraic number) and both pi and e are known to not be algebraic.