Is there an algebraic solution for the to find the intersection of the following two functions for values of $x\geq 0$:
$f_1(x)=1-2e^{-x/a}=f_2(x)=-1+2e^{-x/b}$
$a$ and $b$ are positive constants.
The equation can be simplified to:
$e^{-x/a}+e^{-x/b}=1$
A Plot is here:
I am searching for the $x$-value of the intersection in the second plot (this is for an inversion recovery experiment inf magnetic resonance).
If there is no algebraic solution, can you suggest a numerical algorithm for this problem?
Thanks