To keep it general, I want to solve
$$ a = t - be^{ct} $$
where $a, b\text{ and }c$ are known real numbers. I cannot find an analytical solution for $t \in \mathbb{R}$ and I am wondering if there is one.
2026-03-25 15:59:55.1774454395
Is it possible to solve a simple equation involving linear and exponential components?
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a solution with the known elementary functions is not possible, we Can write $$x=\frac{a c-W\left(-b c e^{a c}\right)}{c}$$ where $W$ denotes the Lambert W function