What is e in this equation, and how do I solve it?

If you're having a hard time getting the same numeric result for that expression, it might be because you're not entering it correctly on a calculator. To get the correct value, you need to use parentheses in the right places.

Using a computer, or a TI graphing calculator, you would enter the expression this way:

e^(-2.91+6.26*0.1)/(1+e^(-2.91+6.26*0.1))

If you do that, you should get the right numeric value.

This is the Euler's constant. It is approximately $2.718281828459$... You can read more on it here:

https://en.wikipedia.org/wiki/E_(mathematical_constant)

Here $e$ is Euler's number, ($e \approx 2.718$) and that is the correct answer to the equation, so you might need to double check your work. If you don't use enough digits of $e$ (i.e. $e \approx 2.7$ evaluates to $0.09375\dots$), then your answer will be off.

Wolfram Alpha confirms that:

$$ \frac{e^{-2.91 + 6.26\cdot 0.1}}{1 + e^{-2.91 + 6.26\cdot 0.1}} = 0.0924568 $$