Hi @Ghofelt, welcome to our forum and I'm sorry to hear about this. 
Most of our devices features a proximity sensor that will turn the screen off during a call when the sensor is covered by for example, your ear and when you take the phone away from the ear, the screen will turn on again.
On page 7 on the link below you can see where this sensor is placed on your Xperia P.
http://www-support-downloads.sonymobile.com/lt22/userguide_AE_LT22i_2_Android4.1.pdf
Make sure that this sensor is not covered by a screen protector or that there is any dirt or moisture on the sensor. If there is, the sensor will not work properly and the phone will not understand that the sensor is not covered any more and you will have to wait for the counterpart to end the call.
You can also try and reboot your phone in safe mode, to make sure that a downloaded application isn't the cause of this behaviour.
In addition to this information, do note that the Xperia has reached it's end of support so our support for this phone model is limited and you will not be able to have it repaired at an authorized service centre / perform a software repair.
Let me know how it went!
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