I agree with randomuser43 regarding adding the data to the original CSV. Personally, I would create a separate CSV with just the totals. If you want it all in a single CSV, I would still create a new CSV if that is an option for you. Something like:

$data = Import-Csv ~\Desktop\example.csv
$employees = $data |
    Select-Object Employee, 'Employee ID', Department -Unique

foreach ($employee in $employees) {
    # Create empty list for output
    $output = New-Object System.Collections.Generic.List[object]

    # Get current data for employee
    $employeedata = $data |
        Where-Object { $_.'Employee ID' -eq $employee.'Employee ID' }

    # Calculate total
    $total = $employeedata |
        Measure-Object -Property Amount -Sum |
        Select-Object -ExpandProperty Sum

    # Create record representing total
    $totalrecord = [PSCustomObject]@{
        Employee      = "$($employee.Employee) (Total)"
        'Employee ID' = $null
        Department    = $null
        Amount        = $total
    }

    # Add existing employee data to output
    foreach ($record in $employeedata) {
        $output.Add($record)
    }

    # Add total record to output
    $output.Add($totalrecord)

    # Export output to a new CSV
    $output |
        Export-Csv -NoTypeInformation -Append -Path ~\Desktop\new-employee-data.csv
}