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There's a constant that is very close to an integer that's referenced here: http://xkcd.com/217/

$e^{\pi} - \pi = 19.9990999$

We nerds find this to be cool because it has two mysterious numbers and it's so close to being an integer.

Well, I got myself into a pickle here when I got curious how much we would need to offset $e$ and $\pi$ to make it come out to $20$. So I set myself up with a single constant $c$ in:

$(e+c)^{\pi+c} - (\pi+c) = 20$

And it occurs to me that I've simply been out of math too long to figure this out on my own. At the same time, I can't just 'let it go' (who does that? What the fool calls inability is what the wise man calls opportunity for growth!)

What steps would I take to solve such an equality?

Note: the tag selection didn't give me much to play with. I would prefer the tag of [Constants] but it's unavailable and alas I can't transfer my SO rep to here. :S

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    Another interesting think on that link, pi almost = ‎(9^2 + 19^2/22)^(1/4)2011-04-09

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Wolfram Alpha gives a value of about 1.84105743 E-5, you can get more digits

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If you have a function $f(c)$ so that $f(0)$ almost has the value you want $y$, then a reasonable next guess is (y-f(0))/f'(0). This is the first step of Newton's method.