Direction of resulting I through simple circuit with 2 voltage sources separated by 2 resistors in series?
The current direction on the diagram is supposed to be the right
  answer


The current direction in the diagram is the WRONG answer.

If you combine those two resistors into a single 100kohm resistor, current flows from the higher potential to the lower potential and the amount is the potential difference (20V-10V) divided by 100kohm i.e 100 micro amps flow from right to left thru the resistor.