Thanks for giving the Friday Brain Game a shot. This one may surprise you. Good luck!

NOTE: After careful consideration (read: complaints!) I've changed the phrasing from "rhyme with" to "share their vowel sound" to make the puzzle more accurate.

What are the only TWO letters of the
English alphabet that, when spoken aloud,
do NOT
share their vowel sound
with at least one other letter?

Here is the SOLUTION.

THE SOLUTION:

O and R.

All other letters rhyme with share their vowel sound with at least one other:

A, H, J, and K have a long "a" sound.
B, C, D, E, G, P, T, V, and Z ("zee") have a long "e" sound.
F, L, M, N, S, X, and Z ("zed") have a short "e" sound.
Q, U, and W have a long "u" sound.
I and Y have a long "i" sound.

O has a long "o" sound, while R has an "ä" sound.