Fix deleted transaction log file in SQL Server
Backup contains the log file as well.

Just restore the database using tsql 

Restore database db_name from disk = ' path to backup file.bak' with replace, stats=10

Based on your screenshot, it seems a connection issue .. you are not able to connect to SQL server with ssms.

Also, see this blog by Aaron https://sqlblog.org/2011/01/14/troubleshooting-error-18456