NY state is a 75% total loss formula state. State insurance statutes as written by your elected insurance commissioner. Doesn't matter who your insurance company is or what Geico's internal policy is, or what your sister's neighbor ran into with State Farm last month in Wisconsin. NY = 75% TLF.
I hate numbers so will keep it simple.
They'll calculate the all-in cost of the claim. Paint, labor, supplies, fees/taxes, rental car. Lets say that number ends up being $8000. $8000 is a realistic number for a complete EL body massage & respray and often panels do need to come off. Unless long-legged and long-armed Adieu can restore a 6X5 foot hood while its atop the vehicle. A black vehicle at that. I've not seen the damage either, but the Expedition EL is no Honda CRV. Its a lot of sheet metal, and if Picasso hit every panel, ....
Then, using previous insurance pool auction data, they'll estimate what a running/driving 2010 Expedition EL Limited, without collision, burn, or flood damage, sells for at auction. Hot tip - Expeditions like this sell very well. Lets say they calculate insurance pool expected result at a modest $6000.
$8000 + $6000 = $14,000 TLF.
I don't know all of OP's specifics to get a NADA value. But again, with simple numbers, if his book value is $18,667 or more, and his TLF is $14,000 - she is totaled. 75% of $18,667 is $14,000. That's the formula. In Iowa its 50%. In Texas it can be as high as 100%.
Lets say I'm high. $5,000 claim + $3,000 salvage price. $8,000. If the book value is $10,667 or more, she is totaled.