In English, "He doesn't show his age" is ambiguous, and it's not the natural way to say either of the possible meanings. It's a peculiar way of saying he doesn't appear to be as old as he really is; the more natural way, for an American speaker at least, would be "He doesn't look his age." The other possible meaning is that he doesn't reveal his age, i.e. he won't tell you how old he is. In neither case would a native English speaker be likely to say "He doesn't show his age."