How to solve for a variable that is the base of an exponential and also a multiplicand on opposite sides of an equation?

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The equation is $$KQ-Kq = nq^n$$ K is known and is a constant. Q will be the independent variable if I can solve for q. n is unknown, but may be considered as a constant and $n\in \mathbb{N}$. I would like to solve for q so I can calculate q as a function of Q for a given n.