Different and opposing voltage sources?
You have drawn a circuit that expresses a logical contradiction, just as much as if you wrote down the mathematical equation

$$5 = -5$$

One way you could resolve this is not drawing contradictory circuits.

If you want to know what happens when you connect two physical power supplies in anti-parallel, then you must provide a more complete model of the power supplies. For example, if you include non-zero internal resistance in at least one of the supplies, you will not have a contradiction, just a very large current produced through the two supplies.