I have a 10-2 wire (Black ,White, Ground) run for a dryer, but the outlet and plug call for 10-3 (White, Black, Red and Ground).

Do I need to change my outlet and hence plug or can I wire this up using my existing equipment?

Thanks,

T

T, appliances are required to be installed in accordance with their installation instructions.
If you don't, you void the warranty and may lose insurance coverage if something happens.
Is there a specific reason you are asking this?

I have a 10-2 wire (Black ,White, Ground) run for a dryer, but the outlet and plug call for 10-3 (White, Black, Red and Ground).

Do I need to change my outlet and hence plug or can I wire this up using my existing equipment?

Thanks,

TYou need to change the wire. 10/2 was never legal for an electric dryer.

Almost every dryer runs on 240 VAC with a 30 Amp breaker. That would be an 8/3 AWG. What breaker is currently connected?

Almost every dryer runs on 240 VAC with a 30 Amp breaker. That would be an 8/3 AWG.Electric dryers in the US are 120/240V circuits, typically using 10/3cu with ground cable.

I agree 120/240 but I have 2 houses with electric dryers running double 30 and 8/3.

I agree 120/240 but I have 2 houses with electric dryers running double 30 and 8/3.That is perfectly acceptable, but it is definitely not typical.
Typical for a 30A circuit is #10 wire.