Can I run an electrical feed to my shed to power an outlet without setting a subpanel. The shed is approx. 75' from electrical service in house and about 50' from house to shed. Can #12, or # 10 wire work without too much voltage lose. Amps to be at 20.

At 50 feet you would lose about 8 volts on #12, and 5 volts on #10. If you are powering lights, or small power tool, you will probably be OK. If you have to bury wire or conduit, you may as well do it correctly and put in a small subpanel. This of course depends on your needs, now or in the future.