Generally, you can't solve something in the following form:$$xe^{x+c}$$because of the stupid "$c$".

If you can't get it into the form $f(x)e^{f(x)}$, it is also probably not solvable.

You usually can't solve $$f(x)g(x)$$where $f(x)$ is more than one "level" away from $g(x)$. For example:$$xe^{e^x}$$has no solution because $x$ is two "levels" away from $e^{e^x}$.

Negative levels can be treated as logarithms.

The Lambert W function does not like addition, which is why you usually cancel addition by exponentiation and applying exponent properties.

Any base is considered fine (usually) because you can change the base with exponent/logarithm properties as well.

Generally, you can't solve something in the following form:$$x^{x+c}$$because of the stupid "$c$".

If you can't get it into the form $f(x)e^{f(x)}$, it is also probably not solvable.

You usually can't solve $$f(x)g(x)$$where $f(x)$ is more than one "level" away from $g(x)$. For example:$$xe^{e^x}$$has no solution because $x$ is two "levels" away from $e^{e^x}$.

Negative levels can be treated as logarithms.

The Lambert W function does not like addition, which is why you usually cancel addition by exponentiation and applying exponent properties.

Any base is considered fine (usually) because you can change the base with exponent/logarithm properties as well.