Root of Equation e^x (x - 1) = e^-x (x + 1)

Theorem
The equation:
 * $e^x \paren {x - 1} = e^{-x} \paren {x + 1}$

has a root:
 * $x = 1 \cdotp 19966 \, 78640 \, 25773 \, 4 \ldots$

Also see

 * Definition:Kepler's Equation