It’s what’s called property damage excess, which means the damages exceed his $10k limit

In short, you’re SOL.

The other totaled car is also going to have to use their collision coverage to get their payout and that company (ex: Statefarm) will subrogate (seek recovery of the amount the at fault party owes) from Geico (other claim).

You’ll be waiting until that process is finished, which will likely be a couple months at minimum (although there is a 3 year statute of limitations). Once the at fault claim gets their bill, they’ll prorate the apportionment of their $10k limit between you & Statefarm.

You need to have the at fault claim inspect your vehicle to get a total loss valuation done so they have it on file when they’re ready to prorate their limits. Keep any receipts from any rental you pay out of pocket or anything else related, you’ll be able to include that in the prorated amount

Sorry! Let this be a lesson on why collision is important insurance to carry :( it’s an expensive lesson to learn but be thankful no one is injured and remember: it’s only a car!