This is possible. EFI doesn't HAVE to be a separate partition.
In this case you have a (hidden) EFI folder located on your C: partition in stead of a separate EFI partition. Or the OEM or Recovery partition doubles as EFI partition as well.
Some pre-installed computers (especially if they also have a recovery system) are setup like this.
If you did a Windows 7/8 upgrade to Windows 10 you can under some conditions also end up with a strange setup like this.
If your computer works fine just leave it be.
If you really want to have standard install you will have to wipe the entire SSD (also remove the OEM/recovery!) and re-install Windows 10 from scratch. It that case it will setup its normal EFI as a seperate partition.
1Are you sure you don't have a System partition? Otherwise, your disk might have been formatted as MBR, rather than GPT, and this caused the installation in legacy mode. Please add a screenshot of the Disk Management. – harrymc – 2018-08-05T13:31:52.030
or run diskpart > list disk to see if the disks are GPT or MBR. Run select disk 0 > list volume to print the volumes of each disk – phuclv – 2018-08-05T13:41:49.793
@harrymc My disks are both in GPT, SSD and HDD, and running msinfo32.exe shew that the computer was booted in UEFI and not Legacy, but that might have been because my HDD is installed at the moment, however it boots even with the SSD only. Tomorrow, as it's late evening now, I will remove the HDD, boot the commputer with the SSD only and tell you what msinfo32.exe says. – Ulisse Benedetti Ulisse54 – 2018-08-05T13:49:25.703
I really prefer Disk Management. – harrymc – 2018-08-05T13:56:59.360
Yep, confirmed, my computer boots in UEFI even with ONLY the SSD in it. Guess I'll just nuke my older drive. – Ulisse Benedetti Ulisse54 – 2018-08-06T06:07:21.047