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Thanks for the update!
If you have already done the above, I'm afraid that the phone has to be sent in to an authorized service centre so a trained technician can examine the phone and repair it.
To have the phone sent to an authorized service centre, contact your local support team and they will assist you with this.
They will also assist you with any questions that you may have regarding service times, routines and warranty.
Hi @Dphilip, I'm sorry to hear about that.
There is a sensor placed on the phone that is called proximity sensor that will turn off the display when you are in a call, to prevent you from ending the call with for example your chin.
If this sensor is covered by a screen protector like @Viridis mentioned or if there is any moisture on the sensor, it will turn off the display directly after you press call and not when it's covered by your ear.
On the picture below you can see where this sensor is placed on your phone, its number 1.
Try wiping the sensor clean with a dry cloth or remove any screen protector on your phone if that is covering the sensor.
You can after doing that try the sensor in the phone in the inbuilt test called Diagnostics which you can find in Settings > About phone > Diagnostics > Test > Proximity sensor.
Let us know how it goes! 
Do you remember if you installed a new application in your phone just prior to experiencing this behaviour?
I'd recommend that you reboot your phone in safe mode, just to make sure that this is not caused by a downloaded application.
When the phone has rebooted to safe mode, place a call and check if it's working or not, or you can run the diagnostics test again.
If there is no change when the phone is rebooted in safe mode, try performing a software repair using Xperia Companion. This will delete all data on the phone and install the latest available software again, since the data is deleted creating a backup prior to starting with the repair is advised.
Let me know if that helps!
Thanks for the update!
If you have already done the above, I'm afraid that the phone has to be sent in to an authorized service centre so a trained technician can examine the phone and repair it.
To have the phone sent to an authorized service centre, contact your local support team and they will assist you with this.
They will also assist you with any questions that you may have regarding service times, routines and warranty.
You're welcome! 
Sorry that I weren't able to resolve it for you, but it's hard when it's hardware related. 
Let me know if there is anything else I can assist you with and I hope everything will work out with the repair!