Differential backup to a specific date in history
If your database is configured for SIMPLE recover model, you're pretty much out of luck.

If your database is configured for FULL recovery model, you might be in luck.  This query will tell you what the recovery model is:

select recovery_model_desc from sys.databases where name='&lt;YourDatabase&gt;'


If your database is configured for FULL recovery, you could attempt to take a transaction log backup (example here). Then, you could attempt to restore your full backup WITH NORECOVERY and then restore your transaction log backup to a point-in-time using the STOPAT option (example here) 

Assuming you can attempt a restore to point-in-time, you should probably restore to a test database to prevent overlaying the current one and then retrieve the missing data from the test database.