Find zero of this exponential equation

Question

I know that you can find numerically answer to this, but is it possible to express x somehow algebraically $e^{\frac{2}{x}}=x$?

Answer 1

$$1 = \frac{1}{x} \mathrm{e}^{\frac{2}{x}}$$ $$2 = \frac{2}{x} \mathrm{e}^{\frac{2}{x}}$$ $$\mathrm{W}(2) = \frac{2}{x}$$ $$x = \frac{2}{\mathrm{W}(2)} \approx 2.34575$$ Where $\mathrm{W}(z)$ is the Lambert W function.

A good tutorial can be found here, where we see that for $a=b\mathrm{e}^{b}$, we have $b=\mathrm{W}(a)$