Job completes successfully and logs the errors to a text file
Create a notification for the Job failure. The below email will help you with the steps:

Step 1 : Configure database mail and do a test if thats working fine.

Step 2 : Change Agent properties 
         Under Mail session, select the option to Enable mail profile. Ensure the correct Mail profile is selected.

Step 3 : Create Operator.
         Under the SQL Server Agent, right-click Operators and select New Operator and configure accordingly.

Step 4 : Under the job properties for the backup, go to Notification tab and select email when the job fails:



Step 4 : 

Notification for job failure