Using external disk for Time Machine

It is possible but it is not recommended.

Time Machine does not need to use SSD. You could get a second HDD (mechanical hard-drive) for very little money. (I'm backing up my Mac using a HDD.)

If you wanted to share a drive, you would need to partition it, one partition for each Mac. Each Mac would then point to their own partition in Time Machine.

You need two "volumes," but not two drives. Each volume is ideally twice the size of the Mac it is backing up. Probably it'd need to be a pretty big drive.

As everyone else said, this is likely a bad idea. I've had more than one Time Machine drive that's ceased to be, had gone to its maker, was no more, became a dead parrot. I'd hate to think that I'd lose two computers' backups all at once.

Things would be tons easier, with a lot less chance of errors, if each Mac had its own external drive for backups.

FWIW I use an external HDD to make bootable backups from several old Intel Macs with Carbon Copy Cloner. But for my main Mac I do use a dedicated external disk (in fact I use two such backup disks, just in case).

One thing not stated "out loud" is asking you the question: Is your backed up data critical to you? If it is, as I suspect it is, then you want to ensure that your overall backup strategy includes multiple destinations for those backups. If not, then just about any backup solution will work.

Ref: macOS Backup Strategy - Apple Community