Dear {Name},
I'm so sorry for seeming distant lately. It wasn't until {you said/incident occurred} that I fully realized what I've been projecting.
In truth, I have been going through a tough time {personally/professionally}, and that is probably what you picked up on. I don't want to burden you with my problems, but essentially {brief explanation}.
I feel fortunate to have a {friend/colleague/family member} as intuitive as you. Most people wouldn't have noticed. I'm glad that you felt comfortable saying something, in part because it's given me the opportunity to apologize for any hurt feelings I may have caused you due to my lack of engagement.
I appreciate your {offer to talk/counselor recommendation/sage advice}. I'll be sure to reach out to you if need be.
Sincerely,
{Name}
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