As you can see, one of inputs of a XOR gate is connected to the output of the same XOR gate. Each time when the output is "true" it influences its input and it makes the gate change output to "false". But when the output is "false" it's redirected to input and makes the gate change output to "true".
As a purely logic circuit, it is unstable and has no solution as is noted in your question.
In practice, logic gates have a propagation delay and a non-linear transfer characteristic. Delay in CMOS chips depends on load capacitance and supply voltage.
Here is an example (PDF), where propagation delay can be around 50ns to 200ns.
So you will probably get an oscillator if you build this circuit. Or, depending on construction and the actual chip, you may end up operating in the linear range of the transfer characteristic (just like an op-amp configured as a voltage follower), so the output may be a stable voltage midway between 0 and Vdd.