Jean Meeus’s statement that it can only be deduced from observations is (unless I’m mistaken) only true for UT1 – a time standard which strictly follows the Earth’s rotation.
The time that the clock on your wall reads is UTC, which is pinned to International Atomic Time (a realisation of TT), but has leap seconds added to keep it closely aligned to UT1.
The quantity you’re almost certainly looking for is (TT-UTC), which is exactly 37 seconds currently, and changes in 1 second steps when leap seconds are added to UTC.
Whilst observations certainly are needed to determine (TT-UT1), it’s not a very useful quantity for most people, because UT1 is only used for a few specific applications that directly involve the Earth’s rotation. The ones that come to mind are calculating precise sidereal time, and calculating the Earth’s rotation angle during eclipses. Oh, and of course deciding when to put leap seconds into UTC! 🙂
If the problem you’re working on involves the times when the Moon is at certain positions in its orbit, then that’s a problem where the Moon’s orbit is defined in TT, and you want to report times in UTC. So UT1 doesn’t come into it.