Try the following. I have provided several options that you might be interested in.
The following is simply your code edited to make it work.
Sub Macro()
Dim myrow As Long
Windows("techdata.xlsm").Activate
Sheet1.Activate
Range("A16").Select 'Need to identify the starting cell first
ActiveCell.FormulaR1C1 = "Sum"
ActiveCell.Offset(0, 1).Select 'Activte one cell to right of starting cell
myrow = Range("E6666").End(xlUp).Row
ActiveCell.Formula = "=SUM(E3:E" & myrow & ")"
Sheet1.Columns().AutoFit
End Sub
However, it is almost never necessary to actually select cells. Most code can be written by simply referencing the required cells like the following code example.
Sub Macro_2()
Dim myrow As Long
Windows("techdata.xlsm").Activate
Sheet1.Activate
Range("A16") = "Sum" 'Need to identify the starting cell
myrow = Range("E6666").End(xlUp).Row 'Last used cell in column E
Range("A16").Offset(0, 1).Formula = "=SUM(E3:E" & myrow & ")"
Sheet1.Columns().AutoFit
End Sub
Both of the above solutions require "Sum" to be in cell A16. If you insert additional rows under your existing data table at the top then it will no longer be cell A16. Therefore if you select the cell with Sum in it and create a name for it by using Formula ribbon -> Define name and give the cell a name (eg. SumCell) then if you insert or delete rows above it then the name assigned to the cell moves with the cell and you can then reference that cell by its name like the following code example.
Sub Macro_3()
Dim myrow As Long
Windows("techdata.xlsm").Activate
Sheet1.Activate
Range("SumCell") = "Sum" 'Need to identify the starting cell
myrow = Range("E6666").End(xlUp).Row 'Last used cell in column E
Range("SumCell").Offset(0, 1).Formula = "=SUM(E3:E" & myrow & ")"
Sheet1.Columns().AutoFit
End Sub
It is even possible to create the entire "Approvals Summary" table a specified number of rows below the last data in the table above. If you want an option like this then please get back to me.