What bothers me about that is that you describe something that should not occur.
Structurally, a UNION query "stacks" two tables of similar structure, one atop the other, and you riffle through them as though they were a single stack. To have too many fields, the 160 fields in each must not overlap completely.
A JOIN with 160 fields in each table would give back 320 fields - clearly too many because of the limit of 255. But a proper UNION of two tables with 160 fields each should yield twice as many records but still of only 160 fields each. So I'm confused.
What bothers me more is that it is rare to need that many fields even ONCE, let alone twice. I suspect that to start this whole shebang, your tables aren't normalized. That is SUSPECT, not AVOW. If you could normalize the tables, you might be able to avoid the problem altogether.
If you are in doubt, read up on "Database Normalization." If you know about that already, all I can say is that 160 is a lot of fields for a single table.