Does anyone know if it's possible to dual wield a trident and a longsword? I'd like to make a character that was an ex-gladiator, and this is all I have to go off of for inspiration.

Take the Dual Wielder feat.

Note: -- it was trident and net, and no gladiator ever used a longsword, traditionally, They all used short swords. That, of course was "real world", and I mean, wtf who cares, right? 

As noted, it would be dual wielding or some similar skill (depending on class). Versatile would be in play for both, but one could only ever use the regular roll, not the additional unless the second was dropped.

Good combination -- decent damage, plus a thrown weapon attack that can be handy in certain bonus action situations.