Is your problem I presume,Originally Posted byfreswood

Let,

Then,

Thus,

Thus,

We can see that is a solution because,

Thus,

thus,

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Though I did not prove it, I believe there are no other solutions because this leads to the Lambert function, but I do not know if this is a high school problem or a problem for Analysis class which your professor want to demonstrate with the Lambert function. If a high school function igonore this entire paragraph.