MHB Which is greater: $e^{\pi}$ or $\pi^{e}$?

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Which is greater, $e^{\pi}$ or $\pi^{e}$?

I found this when searching for calculus inequalities.
 
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A variation of the same method is to raise both numbers to power $1/(e\pi)$ and find the maximum of $x^{1/x}$.
 

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