Yes, it's easy enough to create pseudo-randoms within certain bounds, but it's very difficult if there isn't 'play' in at least one of the bounds, for example, a set of five random numbers from min 5 to max 10 which must total 50 leaves very few options.

This is not to be stubborn, but you've really got to let one of the bounds go to have a chance.

In terms of maths, depending on what you need to keep, solutions can be very simple, e.g.
10 random numbers (0 - 1) in A1:A10 then B1=A1*20000/sum(A$1:A$10) - each number is random, but the are normalised up such that the sum of the random numbers = 20000, but haven't fixed start or end points.

So, what could we lose?