First, you need to access the mailbox on the Microsoft Exchange Server and then get the mailbox statistics for the count of e-mails. The credentials you use should have admin access on the Server to be able to access the mailbox.

The following script uses some credentials stored in a file on the machine where the script is running and connects to a Session on the Microsoft Exchange Server:

$un = “admin@somedomain.com”
$Pass = cat “C:\Temp\Securestring.txt” | ConvertTo-SecureString
$Credentials = New-Object -TypeName System.Management.Automation.PSCredential -ArgumentList $Un, $Pass

$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri http://{servername}/PowerShell/ -Authentication Kerberos -Credential $Credentials

Import-PSSession $Session -DisableNameChecking

$data=Get-MailboxFolderStatistics -Identity "somemail@somedomain.com" -FolderScope inbox | ?{$_.folderpath -eq "/inbox"} | select ItemsInFolder 

Write-Host $data.ItemsInFolder

You can further use this data item to mail it to the Admins for Operations purpose.

To know how to send e-mail in PowerShell, check out this post here.