Hi OP. I'm so sorry this has happened. Take deep breaths, you will feel ill and in shock. this will pass and is a physical effect. Just go through some actions. Photograph or even just write down the most incriminating texts, including the times and dates they were sent/received. Write down the phone number.
If there is only one phone number that this phone is being used for and it was hidden, there is no other explanation. Do not allow yourself to think you are mad. You're not.
You can then do one of two things. You can talk to him or call the number. The best thing to do is to talk to him. If you need to check if this is still ongoing (i.e there are no recent texts, you could text the number as if from him to see what/if there is a response. If there are relatively recent texts, don't bother.
Do not call him. The conversation you have with him should be in person if AT ALL possible and he shouldn't get wind of something being wrong, if you can bear it at all.
All cheaters lie when confronted. So bear this in mind. He will try and make you feel crazy. He will deny, sometimes quite realistically.
If you ask him about the phone, he won't know you've looked on it necessarily and may lie about having 'found' it. Remember he had hidden it and it has one number on it. This is not going to be true.
The best approach is to make open, demanding statements like 'Tell me everything about this woman. Now.' Try and be calm, although it will probably be impossible. He may break down/walk out or probably just feign ignorance and lie over and over. If he tells you any truth it will be minimised. He will ask you questions and distract from the matter, 'What were you doing looking through my stuff?' This is all irrelevant and should be ignored. Go back to the demanding statement. Any lies should be greeted with continual 'You're lying. Tell me the truth. You're lying. You're lying', as calmly as you can. YOU ARE NOT MAD. This has happened. You can google the number just in case, and you can call it to see if you get an answerphone if you like, but don't talk to the woman. She will probably alert him somehow.
I am so sorry again and don't lose control totally. You just need to get through this stage and you will have more information. You can come back here and we will help you through it. Don't let your mind wander too far into the future. He needs to tell the truth first.