A carbon-carbon bond requires 348 kJ/mol to break. What is the minimum frequency of radiation with enough ene

The C-C bond is strong, the strength you quoted need not be the radiation that can break it -strength vs strength is not the sole criteria in this. The environment- temperature, catalyst , presence of 'other groups' attached to both the C's,- all contribute to its survival/ destruction ! In theory, we can break a bond with say 10 % extra radiation energy, but it is never a sure occurrence. [Pl. see the best range of radiation from your text , or your teachers]
Thus in the C-H bond in (C6H5)3C-H is so easily 'broken' - it remains, under optimum conditions as a couple of free radicals, or C-+H+ pairs.[Both the radical & carbanion are stabilized by the 3 benzene groups; similarly [(C6H5)3C-]2 also exists in dissociates free radical form !
Again, pl. see the iodoform reaction - alkaline I2 in water oxidizes ethanol to acetaldehyde, later to
CI3-CH=O, & later to CHI3: The CI3 group is so easily split off - the C-C bond is broken at room temperature ! Here the 'leaving group' , solvent, the rest of the molecule - all play an important role !