Word (unlike WordPerfect) doesn't do that with paragraph alignment. Set the
paragraph to left alignment, and insert a right-aligned tab stop at the
right margin. Enter the left element, followed by a tab character, followed
by the right element. Here's a sample of code:

Sub demoLeftRight()
   Dim rightMarginLocation As Single
   With Selection.Sections(1).PageSetup
       rightMarginLocation = .PageWidth - .LeftMargin - .RightMargin
   End With

   With Selection.Paragraphs(1)
       .Alignment = wdAlignParagraphLeft
       .TabStops.ClearAll
       .TabStops.Add Position:=rightMarginLocation, _
           Alignment:=wdAlignTabRight
       .Range.Text = "left stuff" & vbTab & "right stuff"
   End With
End Sub

Note that if you're trying to do this in a header or footer, the default
styles for those areas (named Header and Footer) already have the tab stop
defined this way, so you don't have to do it in code.