Irrational numbers.

Note that $(x+e) (x+\pi)=x^2+(e+\pi)x+e\pi$ , so if the numbers $e+\pi$ and $e\pi$ were both rational, $\pi$ and $e$ would be the roots of a polynomial with rational coefficients and hence they would be algebraic numbers. But that's impossible because $\pi$ and $e$ are both transcendental numbers! So at least one of the numbers $e+\pi$ and $e\pi$ is irrational.

NOTE: It is still an open problem whether $e+\pi$ is irrational and whether $e \cdot \pi$ irrational (see, for example the MathWorld Wolfram page on e ).