Those are the only numbers you need.

You have a standard "700C" road tire. Most tubes you can buy will fit a narrow range of sizes, and you will probably need one that is labled "700 X 18 - 25" or "700 X 20 - 28" or similar.Tubes can stretch so if you get one labled "700 X 18 - 23" it will still work in your 25mm wide tires.

The only other peice of info you need is the valve type. Most road bikes have the narrower "Presta" valves, but the larger car-type "Schreader" valves that can be easily filled at a gas station are also common.

Also, if your rims have an exceptionally deep-V cross-section you might need a tube with a long valve.