I am sorry to hear you are having problems with the system but let me help you.
The reason why you are not able to set this resolution might be because the TV does not support it but I would like to confirm this.
I recommend you updating the drivers for your NUC. Here you have the latest driver:
Besides the step above, it is important to update the BIOS in your system. Here is the link:
Once you have updated the drivers, please post your Graphics report. How to get it?
Graphics Report: Open Graphics & Media Control panel> Support Options> Information Center> Save> Copy/paste
With this information I can see the supported resolutions by the TV.