SQL Server Agent won't be doing the backup. SQL Server will. You'll have to assign the SQL Server service (mssqlserver) a domain account that has rights to the network resource.

I'm also not sure if the SEM will "see" mapped drives. You're probably going to have to explicitly specify the path and file in the backup command

BACKUP DATABASE mydatabase TO DISK='path&file' ...

Have you tried the Maintenance Wizard?

-Mike