Literally, in French, I guess this is "to decide the subject."

The translation "It is impossible to resolve the issue" seems to be, in general, a very good rendering of the meaning. This is definitely the closest idiomatic phrasing of this general statement that I can think of.

The only other options I can think of for close translation is "It is impossible to settle the matter", or you could say "settle the issue" to equal effect.

If you venture out for looser translations of meaning and changes in construction, then there would be, of course, many options, but the best verb choices that carry the intended meaning are "resolve" or "settle." Reasonable translations for "subject" include: "issue," "matter," or "case."

While the use of "determine" or "decide" would ultimately create an accurate enough meaning, in English it is subtly harder for something to be "impossible" to decide or determine unless there is a problem with the will or assertive capacity of the speaker to pick a winner. ("Of course it is impossible for you to decide, you silly man! You are slow and weak! If you were more like your father, you would not find so many things impossible!")

Where the meaning to be conveyed is that "the dictates of reason" make it "impossible" for an opinion of correctness to be formed, the actions of "resolving" and "settling" more aptly reflect what is involved.

Because the impossibility if "deciding" or "determining" something tends to slightly imply that there is something wrong with the "decider," you would then need to add some qualifiers to avoid the implication, as in "Logically, it is impossible to decide which approach is correct." You have to say "logically" in this instance to qualify the decider as something other than an idiot or weak-willed namby-pamby (now, there's a word!).

When you use "resolve" or "settle," doing so fits better with the passive construction of the original sentence. These terms help reinforce the idea that "the math just doesn't work out," the reasoning simply doesn't resolve, the dust simply doesn't settle, this is a messy situation, it's simply the nature of the thing -- it's not the decider's fault; no, it just can't be done, good judgment makes it so: it is impossible to decide this case.