If the database is the only thing running on that system AND you weren't doing some kind of system backup on the 18th or don't have another cause for the CPU spike, here's what I'd recommend.
In DPA, click on the 18th. Set the Interval to be 1 day. Click on the one vertical bar. Select the Waits tab. Click on the CPU/Memory wait/activity.
You should see all of the SQL Statements contributing to the usage. Look for the big bars. 8 )
Now do the same for the 19th and 20th and hopefully you'll see what's causing the delta.
For the statements using the most CPU, start to look at the workload stats (click into SQL with big bars and look at logical reads, executions, etc.).
That should help you as a DBA build the story of what happened on the 18th.