...subtracting twelve maintains the same odds with ties 'succeeding' for the rolling adversary; some DMs instead subtract eleven and flip ties for the PC to always win, which is mathematically identical, but then you have to keep track of flipping tie-resolution back-and-forth depending upon who's rolling...

Perception +6, Trap DC 14 = Passive Perception 16, Trap +2
(both have the same 65% chance of detection, 35% chance of staying hidden)

...it becomes a pretty trivial exercise to invert any roll after you've done it once or twice...