I came across this question in my exam, however I have exactly no clue on how to come across it.

''If the numbers

$\displaystyle e,\pi ,\pi^2, e^2,e\pi, $are irrational,

prove that at most one of the numbers

$\displaystyle \pi+e, \pi-e, \pi^2-e^2, \pi^2+e^2$is rational.''

I think the person who gets a solution to this deserves a prize