I completely understand that this has highlighted risk. I also completely get that you are not an unreasonable, insecure jealous woman. It frustrates me intensely when I see posts wailing about why can't women and men be friends or tacitly putting the blame on the partner who's discovered a secret. Your responses are in fact entirely healthy.
This isn't about lovely, safe friendships of the kind I've described with my fellow football-loving male friends.
This is about friendships that have the capacity to threaten because the boundaries have become blurred. As soon as any element of secrecy has entered the friendship, a boundary has been breached. So neglecting to tell you OP that this woman even existed and that he was in text contact with her means secrecy. Deleting texts adds to that. Secondly, if there is physical chemistry present between the secret friends, this is another boundary crossed. Thirdly, if intimacies that would normally be reserved for a partner are being shared, this is the ultimate barrier crossed.
It sounds as though what you read felt too intimate and personal for work friends and I'm sure you're right. What you haven't seen though is what your H was sending back, or learned why he encouraged this friendship, when he couldn't pretend this woman just wants to be friends with everyone. I'm sure we could all have a good guess....and it's precisely why he kept this woman secret. He cannot run the defence that he couldn't tell you because you are a jealous harridan. I'm assuming you would laugh out loud and call him on this ridiculous form of counter-attack...
So he cannot run the "innocent man" defence or the unreasonable wife ruse. So what he's left with is what is invariably the truth. And it doesn't mean he's a bad man or that you've got a crap marriage either.
I expect this flirting felt reasonably safe and that it has been making the days go quicker. Her texts probably make him smile and this combined with what I imagine will be a lot of flattery and mirroring in real life, is no doubt giving him an ego boost and a spring in his step. He might enjoy going into work a bit more right now. However, this is how the addiction to the new friend starts. The next boundary could be admitting how attractive they find eachother, finding opportunities to work together/have lunch or coffee alone and so it goes on. At this point people in denial will bargain; "Well, I couldn't very well say I found her unattractive could I? So I said that yes, she was gorgeous." or "What's the harm in lunch or coffee? It's what friends do isn't it?"
The absolute must in these situations is that he comes out of any denial and admits to how he has been feeling. If he minimises this or claims innocence, this can happen again and again. You in turn need to promise understanding because this could happen to any of us.
It's much easier to cross boundaries if life is tough and people are in need of an escape, not necessarily from their marriage but the stress of modern life. It is especially easy though if there is reduced intimacy and honesty in your marriage. And this is why this could happen to anyone because we will all have stressful times and most marriages go through a dip at some point too. And unless someone is deeply unattractive inside and out, we are all likely to meet someone who is attracted to us and isn't bothered about a wedding band, partner or children. Most people will get an opportunity to be unfaithful at some point, but wise souls know the risks and swerve situations before they get out of hand. They know their boundaries and their own (very human) weaknesses.