odd mortgage question

A standard mortgage question is: if you know the monthly interest rate
r, the length L of the loan (measured in months), and the principal y,
what is the monthly payment P? (Assume everything is compounded
monthly.)

I know the answer to this, and it's easy to compute or look up
anyway. The formula is

P = yr (1+r)^L / ((1+r)^L - 1)
= yr / (1 - (1+r)^{-L})

*My* question is: if you know the length L of the loan, the
principal y, and the monthly payment P, can you determine the interest
rate r (in closed form)? That is, if you view y and L as constants,
can you find the inverse to the above function of r, say when r is in
the interval [0,1]?

I actually want to compute this in real life, and I can do it
numerically, but that seems so inelegant...

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