"Approximate lookup formula" that returns a value from another cell

Greetings guys;

I'm trying to find a formula that will look in column A, and if it matches a value in col E, it places the corresponding value (which will come from column F), into the adjacent cell in B. Attached is the example and it will make sense when you see the visual. I have added four examples, note the first two highlighted that illustrate what I'm trying to accomplish.

The issue is, the values in E and A don't match exactly. Theyre cities and states; some have ZIPs in the cell, some have commas, others don't, etc.

I feel it can be done with wildcards and maybe XMATCH? Whatever the answer is, I can't figure it out. Let me know if you can solve it and thank you.

Thanks; I'll check it out.