Can Excel show a formula and its result simultaneously?

I'm not aware of any built-in functions for this. You can, however, create a user-defined VB function to accomplish what you want.

Press Alt+F11 to open the VBA editor, right-click in the Project Explorer and select Insert -> Module. Paste the following code:

Function GetFormula(cell)  
  GetFormula = cell.Formula  
End Function

Now you can use =GetFormula(A1) to show the formula of that cell.

Perhaps worth noting that as of Excel 2013, there's a native function for this: FORMULATEXT.

From support dot office dot com article on FORMULATEXT function:

Description

Returns a formula as a string.

Syntax

FORMULATEXT(reference)

The FORMULATEXT function syntax has the following arguments:

• Reference Required. A reference to a cell or range of cells.

Remarks

• The FORMULATEXT function returns what is displayed in the formula bar if you select the referenced cell.

Here’s a way to automate what you were doing before.  It combines the best parts of LonelyKnight’s answer to his/her own question, Indrek’s answer, and Billis’s answer:

Sub Show_Formulas()
    Dim rng As Range, cell As Range
    row_offset = 10
    col_offset = 0
    Set rng = Range(Cells(1, 1), Cells(5, 7))

    On Error GoTo ErrHandler
    For Each cell In rng
        cell.Offset(row_offset, col_offset) = "'" & cell.Formula
    Next cell
    Exit Sub

ErrHandler:
    MsgBox "The cow jumped over the moon", , "Error!", Err.HelpFile, Err.HelpContext

End Sub

For every cell in the specified range (here hard-coded as A1:G5), it copies the cell’s formula, protected by an apostrophe, to a cell a fixed offset away.  (See How do I add VBA in MS Office? for guidance on using VBA in Excel.)  You just have to remember to run this macro before you print.

Or, add a PrintOut , , , True statement just before Exit Sub, and this macro will print the sheet for you.  (You just have to remember to print using this macro.)  The fourth parameter to PrintOut is Preview, set to True to have Microsoft Excel invoke print preview before printing the sheet (thus giving you the option to cancel) or False (or omitted) to print the sheet immediately, unconditionally.

Or, if you’re really concerned about forgetting to run this, you can use Private Sub Worksheet_Change to update the displayable formulas any time you make any change in the worksheet.