Re-wire 2 wire 220 outlet for a 4 wire plug

Hello,

Here's my 'simple' problem. Someone gave me a washer and dryer. I already have a set. Thought I'd just put the news set on patio till I could sell. I could show they work because I have a 220 outlet there. After I rented a truck and got the appliances on my patio I remember a voice from 20-25 years ago. A repairman saw the plug and said someone used to do welding. Hmmm

First step was to verify this outlet did have 220, got a tester - yep, 220. Went to store and got special 4 prong outlet needed for this dryer. Read new plug instructions. Took off old plug cover to look at wires. Looked at disconnect box. Yep - 2 wires. Only. Two wires from the double switch in the box to the outlet. No ground or neutral. This new dryer is all fancy - computer control board and so on. I don't want to fry this dryer by not having the wiring correct at the outlet!

I'm not an electrician. I don't really want to be messing inside the disconnect box. My current dryer uses a 3 prong plug.

I can run an extension cord for the washer to get it to work. How can I easily show this golly-gee-wiz fancy dryer works so I can sell this matched set?

I've been unemployed for 5 months so I don't have much money to spend to get an electrician to make that outside plug have 4 wires for a very temporary usage?

I'm open to suggestions for what I might do.

Sincerely,
bamakodaker

Re-wire 2 wire 220 outlet for a 4 wire plug