You can use PowerShell in conjunction with the Windows Backup command line utility, wbadmin.exe. The code below should help get you started. I have included the date in order to help maintain multiple back ups, but if you do more than one back up per day,
you will need to change the date format to include the time. You cannot control the built in logging of Windows Backup, but you could collect your own backup information and write that out to a text file. As far as sending emails, look into the Send-MailMessage
cmdlet including the -Attachment parameter that could send your log file with your mail message. Cheers.
$Date = Get-Date -Format 'MM-dd-yyyy'
$Path = "\\server\share\$Date"
New-Item -Path $Path -ItemType Directory | Out-Null
Start-Process wbadmin.exe -ArgumentList "start backup -backupTarget:$Path -allCritical -vssFull -quiet"