Years ago, I fitted enlarger lenses to high-speed photofinishing printers I using this this math. It proved accurate enough.
Now for the gobbledygook:
The negative carrier masks the negative plus we desire some over-spill at the easel. I use an over spill of 1.5% otherwise easel placement to avoid shabby borders is laborious.
We now figure magnification based on the cropping of the negative by the negative carrier and factoring in the over-spill.
A 35mm negative measures 24mm height by 36mm length. The negative carrier crops these dimensions, , we will use 23.5mm height by 35.5mm length.
Since we desire an 8x10 inch print, we will use, for the paper size 203mm height by 254mm length.
To figure the needed magnification we divide paper dimension by negative dimension. The 35mm frame is an elongated rectangle, the 8x10 paper size is more square. We must calculate the magnification requirement for both height and width and then use the greater value.
For height: 203 ÷ 23.5 = 8.64X
For length: 254 ÷ 35.5 = 7.15X
We choose 8.64X and apply a 1.5% factor to allow some over-spill.
Thus 8.64 X 1.015 = 8.77 we will use 8.77 as the desired magnification.
Now we compute lens to negative distance base on focal length lens and magnification required. This task places the lens further away from the negative than the focal length. In other words, to achieve this magnification, we compute the back-focus distance.
Say we mount a 75mm enlarging lens.
Next we compute the lens to negative distance based on published lens focal length and operating magnification.
Back-focus distance: focal length multiplied by magnification plus 1 divided by magnification. This is the lens to negative distance.
For a 75mm lens magnification 8.77X:
75 X (8.77 +1) ÷ 8.77
75 X 9.77 ÷ 8.77 = 83.6mm
This answer i.e. 83.6mm is approximate but good enough for what you want to accomplish