ISA Temp at FL330 is approx -51C
If the "OAT" given in the question is -24C, then that has to be RAT or TAT.
Temp rise given is 20C which then gives a SAT of -44C
I don't have access to an E-6B or CRP-5 but an on-line calculator gives a TAS of 459.
I guess if you correct for compressibility you would get close to the 437 that your colleague gave you?
Edited to add that I just found an on-line compressibility correction chart which shows a 12kt correction to CAS. Plugging in 262-12=250 EAS gives a TAS of 438