  The treated matrix equation $(1+ae^{-\frac{\|X\|}{b}})X=Y$ in this short note
has its origin in a modelling approach to describe the nonlinear time-dependent
mechanical behaviour of rubber. We classify the solvability of
$(1+ae^{-\frac{\|X\|}{b}})X=Y$ in general normed spaces $(E,\|\cdot\|)$ w.r.t.
the parameters $a,b\in\mathbb{R}$, $b\neq 0$, and give an algorithm to
numerically compute its solutions in $E=\mathbb{R}^{m\times n}$,
$m,n\in\mathbb{N}$, $m,n\geq 2$, equipped with the Frobenius norm.
