The F10 error code indicates that the electronic oven control board detected a runaway temperature in the oven through the temperature sensor probe. This can be caused by a failed sensor probe or a bad electronic oven control board. A technician is normally needed to diagnose and repair this type of failure.
If you have the technical ability to disconnect electrical power to the range and access the temperature sensor probe, you may be able to diagnose and repair this problem yourself. The oven temperature sensor probe protrudes through the back wall of the oven. To access it, you normally have to remove the back panel of the range. Without a full model number, I am unable to provide specific access information. The probe should have a wire harness plug that can be disconnected. Using a volt/ohm meter, you can measure the resistance of the temperature probe (with the range still unplugged or disconnected from electrical power). You should measure about 1100 ohms of resistance at room temperature. If the resistance is significantly higher, then the sensor probe will need to be replaced. If the sensor probe is okay, then the probe will need to be plugged back in and the resistance will need to be measured through the sensor wires that plug into the electronic oven control board. If the resistance is okay through these wires, then the electronic oven control board will need to be replaced. If you are not completely confident in your technical ability to safely access and check these components, I recommend calling a service technician to repair the range. If you need more specific technical help with your model of Kenmore range, resubmit your question with the full model number and additional details.