After a demanding multi-day hiking trip, I normally try to take as many days off as the trip was long. So that would be 10 days off in your example.
If you felt sick the first week, I wouldn’t count that as recovering from your trip. And it is probably a sign that your trip was pretty demanding for your body.
When I get back to training, I normally do rather short Zone 1-2 sessions for 3-4 days without really having a structure, just to see how it feels. If it feels good, I start regular training with about 50 % of what I did before the trip for a week, if this works fine I might jump back to 100 % the next week.
I was surprised how long it takes to get back to my normal training after a demanding multi-day trip, but this seems like the only way it works for me.