This sounds like an URI (upper respiratory infection). Common signs are sneezing, nasal discharge, red eyes and ocular discharge. The most common pathogens are Herpes virus and Chlamydia. Both are highly contagious between cats and your other cat is probably already exposed- it depends on his immune system if he will become clinical.
The virus will run it's course over 1-2 weeks. If eating/ drinking well then there is not much you'll need to do. If the nasal congestion gets bad, they will likely stop eating and antibiotics are indicated to treat any secondary infection (I prefer Clavamox for this). Another thing you can do is run a hot shower and put the cat in the bathroom to let the humidity break up any debris.
I hope this helps, let me know if you have any other questions.