How do I prove this transcendental equation has a solution? I am trying to prove that for the following equation, there is a B that solves it (c is a constant):
$1-B = e^{-cB}$
I understand this is a transcendental equation, but how do I prove there is a B that solves it?
I need a non-zero solution. c > 1

Note that for $c \gt 1$, for $B$ slightly greater than zero $1-B \gt e^{-cB}$ (you can use the derivatives to show this).  At $B=1$ we have $1-B \lt e^{-cB}$ and there must be a point where they cross.
