How long would it take to get 10 Soleils?

That's a difficult question to answer since it's heavily RNG based. If you want to have a max merge Soleil, this would be your best chance to jump on it.

Last banner I spent 140 orbs for one 4* Soleil, a bunch of Roys, and somehow got 2 5* Hinata before I quit. This time I tried again and got 4 in <50 orbs. If you need an immediate +10 it could get pretty expensive, I decided to not push my luck any further and stopped at enough to +8 and plan to let the last two copies (hopefully) trickle in.

If you go for a 4 star 5 star banner, it shouldn't be horrible. This one only has 3 red units, so trying specifically for reds would give you about 4.5 orbs spent per red pull. With that amount, you have a 32 percent chance of pulling a focus on the 4 or 5 star banners, which of course goes up the more you try. That combined with the minuscule chance that you pull soleil outside the focus would probably give you something of a 36 percent chance average over many pulls to get focus reds. Since Soleil is only one of those reds, you have a 12 percent chance to get her. Since you need to get 10 of them, we would be talking 10*(1/.12)*4.5 which gives 375 orbs. Keep in mind you would pull quite a few other 5 star and useful 4 star units along the way, so it isn't like you're spending 375 orbs just to get Soleil, but that would be the end result. Note that the other two red orb focuses, Cain and Hinata, are not particularly good, so it is probably worth waiting if you know for sure that the next 4 star banner will have Soleil. Whatever you end up doing, good luck with your pulls!

If your lucky? 10 summons. But seriously, you never know, its luck. I've only pulled a few Soleils, and i haven't got a single one from this fodder banner

RNG will decide your fate. You might get 4 in a single circle. You may dump 100 orbs and get 0. But the odds are in your favor right now compared to any other time.