Derivative problem

You equation can't be solve by elementary means, so Prime can't find a symbolic solution.

But if you provide values for U, R and t you can get a numerical solution for L:

This is probably not the solution you are looking for, but when forced to switch into float mode, the symbolic will only return one solution with no control over it.

Note that I used the prime operator for the derivative.

Another way would be to use the usual derivative operator as you did and assign the result to a new function (I called it "f1" in the pic below and made it dependent on t AND L).
You may add units and use the numeric "root" command instead of the symbolic solve. Numerical methods like "root" or a solve block a native to Prime and can handle units (the symbolics doesn't know anything about units):

Prime 6 worksheet attached