Heres the answer:
Assume Linked Server Name: LinkedDB
Linked Server Properties
Check Yes for Collation Compatible
Check Yes for Data Access
Check Yes for RPC
Check Yes for RPC Out
Check Yes for Use Remote Collation
Assume we are subtracting one from the Quantity column of the Inventory table for part-no=1234.
UPDATE LinkedDB..PUB.Inventory
Set Quantity = OPENQUERY(LinkedDB, 'Select Quantity from PUB.Inventory where "Part-No" = 1234') - 1