Chasbo first I would try locating the correct Drivers for your Laptop/Desktop directly on HP website. Since you have an original Windows 8 machine they will have HP's latest Win 10 drivers for your hardware there.
Also check Win 10 settings to set it for Headphones as your sound device. (assuming that's on you intend to use sound)
HP lists the computer as a win 8 computer. I couldn't find anything there. Good idea but.....
Also, you haven't said. Did the headphones in question work before the upgrade? Have you checked them elsewhere?
When you right click on the little speaker icon in the taskbar and look at Playback devices the only thing that shows up is speakers. When you go to the Realtek HD Audio Manager the front panel jacks are grayed out. The only thing that works is uninstalling Realtek but it keeps coming back. The computer has sound through the speakers just fine, When the computer had win 8 and win 8.1 it was fine. This has happened since going to win 10. I can live with this. Apparently other people have had the same problem as I have seen a bunch of info about it online. Either Realtek or Microsoft will hopefully fix it going forward.