Got it. I'll scale things for making 30 mL.
Materials available:
10% nicotine in VG
VG
PG
Make 30 mL of 18 mg in 70/30 PG/VG
The volume you're making and the resulting nicotine level you're looking for will determine the volume of the 10% nicotine in VG you'll be using. In this case, you're making 30 mL of 18 mg/mL, so the mg of nicotine required will be 30 mL * 18 mg/mL or 540 mg of nicotine. Since each mL of your 100 mg/mL base contains 100 mg of nicotine, you'll need 5.4 mL of your 100 mg/mL base.
To be precise, you have to realize that this 5.4 mL contains some VG and some nicotine. Since it's at 10%, and nicotine can be easily enough assumed to have a density of 1 g/mL, this 5.4 mL can be calculated to contain 0.54 mL of nicotine and 4.86 mL of VG.
So, when you put the 5.4 mL of your 10% nicotine in VG into your bottle, you're adding the the following:
0.54 mL nicotine
4.86 mL VG
So, you know you're making 30 mL, and you know there's going to be 0.54 mL of nicotine in that 30 mL. So in that 30 mL, there's going to be 30 mL - 0.54 mL of stuff that's not nicotine, or a total of 29.46 mL of VG plus PG. Since you want 70% PG, you'll use 29.46 mL * 0.7 or 20.62 mL of PG. Now, all you have to figure is how much VG to add. The total VG is 29.46 mL * 0.3 or 8.84 mL of VG. Realizing that the 5.4 mL of the 10% nicotine base contains 4.86 mL of VG already, you subtract this 4.86 mL of VG from the 8.84 mL figure and come up with 3.98 mL of VG.
So, putting it all together into a recipe.
30 mL of 18 mg nicotine in 70/30 PG/VG using a base of 100 mg/mL nicotine in VG:
5.4 mL 100 mg/mL nicotine in VG (0.54 mL nicotine, 4.86 mL VG)
20.62 mL PG
3.98 mL VG
Adding all of these volumes 5.4 mL + 20.62 mL + 3.98 mL = 30 mL
Verifying the critical nicotine concentration, we get 5.4 mL * 100 mg/mL = 540 mg nicotine total
This 540 mg nicotine ends up at a final volume of 30 mL, or 540 mg / 30 mL = 18 mg/mL
Finally, the PG is present at 20.62 mL out of a total PG plus VG volume of 29.46 mL
This gives us: 20.62 mL / 29.46 mL = 0.7 or 70%.
Or looking at it conversely, the VG is present at 4.86 mL + 3.98 mL out of a total PG plus VG volume of 29.46 mL.
This gives us 8.84 mL / 29.46 mL = 0.3 or 30%.
If you ignore the fact that some of the 100 mg/mL nicotine in VG is nicotine, and just calculate it as all VG, it makes the math somewhat simpler and doesn't affect the desired 70/30 PG/VG ratio all that much. Then it just becomes:
5.4 mL 100 mg/mL nicotine in VG
30 mL * 0.7 PG = 21 mL PG
30 mL - 5.4 mL - 21 mL = 3.6 mL VG
