Gelfond's Constant minus Pi

Theorem
Gelfond's constant minus $\pi$ is very close to $20$:


 * $e^\pi - \pi \approx 20$

which is nothing more than an amusing coincidence.

Proof
We have:
 * $e^\pi \approx 23 \cdotp 14069 \, 26327 \, 79269 \ldots$


 * $\pi \approx 3 \cdotp 14159 \, 26535 \, 89793$

Then: 23.14069 26327 79269 - 3.14159 26535 89793 - 19.99909 99791 89486 -