I have a range that needs 10/3 wiring w/ ground... My question is can I just run an additional 10/2 wire... Or do I need to run a new 10/3 wire
electrically speaking yes it is possible to run a just a new 10/2 wire and only use the black (or white) as the other hot but in order to do so that new hot wire would have to go onto a breaker on the opposite side in the load center (fuse box) so it's 180° out of phase giving you 240v between it and the existing hot wire. I say this to help you understand real reasons why not to do it, other than say "against code". First you are running another wire regardless so run the right size ?/3 wire because everything will be easier and simpler. Biggest reason is if you split the 2 hot legs to separate 1-pole breakers, they will never both trip. Only one will ever trip even if both are the same amperage, being a real safety hazard because one leg will always remain hot at 120 volt above ground. That's why you use a 2-pole breaker which is one unit which will always disconnect both hot legs coming off it when it trips. And then if you did run two separate NM-B wires at that 10 gauge size (but connected the hots to a 2-pole breaker) you would not be able to physically manage the extra wiring at the oven receptacle not to mention it would be against code for NM-B. But if you have conduit and ran THHN wire then yes you would simply pull another THHN wire alongsidse the existing to get your extra hot conductor, or neutral, or extra phase in a 3-phase load. But you said 10/2 and 10/3 so this basically means sheathed NM-B and not THHN in conduit.
if the oven is 240v only then you still use a 2-pole breaker in the load center not exceeding the amperage of what the wire can handle. But In this case you can use the existing 10/2 wire with black to one pole and white to the other pole of this 2 pole breaker, both white & black become hot wires with 240v between them.
you said needs 10/3 wiring so that should mean 120v required in addition to 240v at the oven, so u run 10/3 wire which will have black, red, and white plus the bare copper ground. Still need a 2 pole breaker, with black to one pole red to the other pole giving 240v between red and black, then white neutral wire ties to ground in the load center with rest of the neutrals which then provides 120v at the oven via red/white or black/white.
fyi 10/2 or 10/3 assuming NM-B is rated to 30 amps, so you run it from a 1-pole or 2-pole greater less than or equal to 30 amp. 8/2 or 8/3 wire good up to 40 amps, and 6/2 or 6/3 up to 55 amps. So because you're running wire regardless you may want to future proof for any oven and run 6/3 and never have to worry about re-running wire, just worry about the 2-pole breaker size. And if oven not hardwired do a 4-prong range receptacle good up to 50 amp.