Domain ^x+$, match iff there exist perfect powers A and B such that (N - A) is a perfect power of (N - B)

I solved it in ECMA+(?*), and I conjecture it’s impossible in ECMA.

I’m taking “perfect power” to mean an integer ≥ 1 to the power of an integer ≥ 2. The matches up to 50 are 20 (20 - 2² = (20 - 4²)²), 28 (28 - 1²) = (28 - 5²)³, 29 (29 - 5² = (29 - 3³)²), 33, 49

Disregard the last two, I typed them from memory, I don’t have access to my regex to check right now. 33 isn’t in, 41 - 4² = (41 - 6²)².