No, don't.
The problem is that if your Operation class updates the textbox directly, it can't work without your specific form - and that's bad because you can't reuse it, and you can't change the form without considering the effect on the Operation class.
There are two ways to do this:
1) Have a public method (static or not as needed) in Operation that the outside world can call: it does the operation, and returns the result. The outside world is then responsible to using that result to update it's textbox (or whatever else it wants to use)
2) Have an Event in the Operation class which says "result ready" and have the outside world handle it. The outside world then accesses the result via a public Property, and updates itself.
The first way is good for simple operations that don't take long; the second for long running operations that can't return immediately.
To create an event is easy, this explains it:
Transferring information between two forms, Part 2: Child to Parent[
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