How to type the Euro Symbol € on US English keyboard in Windows 10 without a numpad or "AltGr" key?

Yes there is!

You can find all kinds of symbols, including the euro symbol, on the Emoji picker.

1. Go to where you want to enter the symbol
2. Hit WIN+. or WIN+; on your keyboard
3. Navigate to the Symbols tab (Ω)
4. Navigate to the Currency Symbols tab ($)
5. And select the euro symbol. (you might have to scroll once)

This should work in every application accepting keyboard input. After doing this a few times the symbol will show up under "Most Recently Used" as well.

Note that the symbol tab got added in version 1903; if you only get the emojis, consider updating.

Looking for a picture of an HP ProBook 430 which showed a keyboard large enough to read the keys well, I found this image:

It shows an Fn key between the Ctrl key (actually called Strg in this picture, since the picture shows a German version) and the Start ("Windows" logo) key. Hold that down, and then the picture shown indicates M, J, U, 7 correspond to Numpad 0, 1, 4, and 7. So, there is a way to use a Numpad by holding down Fn.

Try holding down Alt and pressing 0128 on the numpad. So, to do that on this computer, hold down Alt, then hold down Fn, and press M. Then, release Fn and hold down Fn again, and press J. Then, release Fn and hold down Fn again, and press K. Then, release Fn, and hold down Fn again, and press 8. Then release Fn. Finally, release Alt. (Yes, you should hold Alt down the entire time.)

If that works well, you may wish to try again by just holding Alt, holding Fn, and typing MJK8 (without needing to keep releasing Fn), and then just release Fn and then Alt in the end.

I use AutoHotKey for this. You can use it for endless customisation but I started using it mainly to get the € and £ symbols on a US keyboard.

https://www.autohotkey.com/

Just create a script with the following, set it to run at startup (Win+R, shell:startup, drop a link to your script in there), and you can then use Ctrl+Shift+4 to get the €. You can remap this to whatever you like, that's just what I picked as that's where the $ is. You can put it on E or whatever if you prefer.

#SingleInstance force

^+4::
   Send, €
Return

It does require additional software but it's easier than the other methods IMO, and if you get into AutoHotKey you may end up using it to create all sorts of other shortcuts, it's very powerful.