Yes, it is possible to recover deleted phone numbers on an iPhone using several methods. The success of the recovery depends on various factors such as the duration since the numbers were deleted, availability of backups, and sync with iCloud or other services.

One method is to restore from an iCloud backup. If iCloud backup was enabled and the numbers were backed up before deletion, follow these steps: Go to Settings > General > Reset > Erase All Content and Settings > Set up iPhone until the Apps & Data screen > Restore from iCloud Backup > Sign in to iCloud > Choose the backup containing the numbers > Wait for the restore process to complete.
Another method is to restore from an iTunes backup. If the iPhone was backed up to iTunes on a computer before deletion, connect it to the computer, open iTunes, select the iPhone, click on Restore Backup, choose the backup with the numbers, and wait for the restore process to complete.
Alternatively, one can restore from a third-party backup such as iMyFone D-Back, Dr.Fone or PhoneRescue. Download and install the backup software on a computer, connect the iPhone, select the backup with the numbers and click on Restore.
If accidentally deleted from the Contacts app, the phone numbers can be restored by opening the app, tapping on “Groups” at the top of the screen, checking if the deleted contact is still available in any other group, and moving it back to the primary contacts group. If not available, tap on “Deleted Contacts,” find the deleted contact, tap on “Edit,” and then “Done” to restore it to the primary contacts group.
Lastly, one can use a third-party data recovery tool such as Tenorshare UltData, EaseUS MobiSaver, or Disk Drill to recover the deleted numbers. These tools scan the iPhone’s internal memory and restore the deleted data, but may not work in all cases and may require the iPhone to be jailbroken, which can be risky and void the warranty.
In conclusion, it is possible to recover deleted phone numbers on an iPhone using various methods, but success depends on several factors. It is always advisable to regularly back up the iPhone to prevent data loss.