insert row in protected sheet by keeping formula

If you just want the result of the formula, try

ActiveSheet.Range("E" & r).Value = ActiveSheet.Range("E1").Value

In the first place: to prevent the users from viewing the macro and seeing the password to unlock the sheet, you must protect the Visual Basic project of the workbook with a password.

• In the Visual Basic Editor, select Tools | VBAProject Properties...
• Activate the Protection tab.
• Tick the check box "Lock project for viewing".
• Enter a password in the Password box.
• Enter the same password in the Confirm password box.
• Important: don't forget this password!
• Click OK.
• Save the workbook.
• Next time you open the workbook and want to view the Visual Basic code, you'll be prompted for the password.

Let's say the password is "secret". The following macro will insert a row and fill down the formula in column C:

Sub InsertARow()

    Dim r As Long

    On Error GoTo ErrHandler

    ' Get the row number

    r = Range("C10").Value

    ' Unprotect the sheet

    ActiveSheet.Unprotect Password:="secret"

    ' Insert a row

    Range("C" & r).EntireRow.Insert

    ' Fill down the formula from above the inserted row to below it

    Range("C" & (r - 1) & ":C" & (r + 1)).FillDown

ExitHandler:

    ' Protect the sheet again

    ActiveSheet.Protect Password:="secret"

    ' Get out

    Exit Sub

ErrHandler:

    ' Report the error to the user

    MsgBox Err.Description, vbExclamation

    ' Always go past the exit handler section

    Resume ExitHandler

End Sub