There are a few problems in your circuit diagram with respect to supply voltages. Do I see -10V on VCC for the op amp? If you are intending to show +/-10V (split supply) on the op amp, then you should have +10V on VCC and -10V on VEE. Also, you show -12V at the inverting input. This is beyond the supply rails of the op amp, and certainly beyond the common mode voltage range of the op amp. Since the op amp model was likely designed to give good results ONLY if it is biased and used correctly, it probably won't give you proper results (models typically give unpredictable results if used outside of normal/proper operating conditions).
That being said, assuming you correct the supply and biasing issues, the simple way to calculate the two switching thresholds would be to simply write an equation that says that the sum of the currents entering/leaving node 2 are equal to zero, and solve for V2.
0 = (V2-10V)/1K + (V2-Vout)/1K + V2/1K
where V2 is the voltage on node 2 that you are measuring, and Vout is the saturated output voltage of the op amp at it's extremes. In the datasheet, these are VOH and VOL - the highest and lowest voltages that the output can swing. You solve the equation twice, once with Vout=VOH and once with Vout=VOL.