A Secant Slope Bound

Let $f(x) = e^x - e^{-x} - ax$ with $a > 0$, and suppose $f(x)$ has two critical points $x_1, x_2$. Let $k$ be the slope of the line through $A(x_1, f(x_1))$ and $B(x_2, f(x_2))$. If $k > -\dfrac{2}{e}$, find the range of possible values of $a$.