GNU Prolog REPL, 57 bytes
(The REPL input ends with two newlines, which are included in the byte count.)
The first line prints the first solution (very quickly, in fact;
fd_labeling often needs tuning to run quickly, but it didn't in this case). GNU Prolog's generates the solution which has the arguments in sorted order first. In this case, only one solution is in sorted order, so we can enter a newline at the "more solutions?" prompt to not generate the remaining solutions; arguably this is hardcoding the number of solutions, but as required by the question, it doesn't hardcode the values in the solution. Uses fixed-point arithmetic (so the numbers are printed without a decimal point), because GNU Prolog's built-in equation solver handles only integers.
This is just a case of finding a language with a language feature that solves the problem almost directly. Mathematica might be the obvious choice, but GNU Prolog has a constraint solver too. If only the REPL ran
fd_labeling automatically! (Come to think of it, maybe I should write a language that uses GNU Prolog's constraint solver behind the scenes and has a terser syntax; it'd be useful in this sort of challenge when it comes up in the future, and possibly even for general use. Oh, and that's designed to solve problems using normal arithmetic operations rather than INTERCAL's.)