I have not used an EU machine on our split phase system, but have done lots of other 240-volt wiring, both here and in Asia. You should have no problem. Most EU/Asian machines have blue, brown and green/yellow wires, which correspond to neutral, hot and safety ground respectively. Here, we have red, black, white and green/bare, which corresponds to hot, hot, neutral and safety ground. Our hot wires are not different phases (industrially we do have 3-phase, but that's a different thing). In our split phase system, the red or the black to the white each give 120-volts. The red to the black gives 240-volts. Thus, to use our power on an EU machine, the brown goes to the red or the black, the blue goes to the black or the red and the green/yellow goes to the frame. You don't use the white wire.

One word of caution is to check with an ohmmeter that there is no internal ground on the machine from the blue or the brown to the frame. There isn't supposed to be (here or in the EU), but one never knows. I suggest checking both because it used to be that European internal wiring was sometimes backwards (brown and blue reversed), I've no idea why. I don't think this is an issue with modern appliances. Another thing to be aware of is that voltage ratings for appliances are "nominal", not actual. It is not uncommon here for our 120-volt lines to be as high as 127-volts, and therefore our nominally 240-volt lines to be 254-volts. Be sure that the EU appliance can withstand voltages this high.

If you search here on H-B, I'm sure you'll find lots of posts about this; I remember seeing them from time to time.

Also consider a 240 volt GFI. Not cheap but safety is worth it.
Dave