Prolog also has constraints! You need to import a library called CLP(FD) / CLP(Z) (depending on the Prolog system) and instead of =, <, =<, etc. you need to use #=, #<, #=<, etc.

    :- use_module(library(clpfd)).

    min(Min, Y, Min) :- Min #=< Y, !.
    min(X, Min, Min) :- Min #=< X.

    find_min_and_subtract_([], [], Min, Min).
    find_min_and_subtract_([H|T], [R|Rs], TempMin, Min) :-
        min(TempMin, H, NewTempMin),
        R #= H - Min,
        find_min_and_subtract_(T, Rs, NewTempMin, Min).

    find_min_and_subtract([H|Hs], Rs, Min) :-
        find_min_and_subtract_([H|Hs], Rs, H, Min). 

With that (and an additional variable for the temporary minimum) it works for me:

    ?- find_min_and_subtract([9,2,4,12], Rs, Min).
    Min = 2,
    Rs = [7, 0, 2, 10]

https://swish.swi-prolog.org/p/qgchfMfB.pl