Right align and left align text in same HTML table cell

If you want them on separate lines do what Balon said. If you want them on the same lines, do:

<td>
  <div style="float:left;width:50%;">this is left</div>
  <div style="float:right;width:50%;">this is right</div>
</td>

It is possible but how depends on what you are trying to accomplish. If it's this:

| Left-aligned       Right-aligned | in one cell then you can use floating divs inside the td tag:

<td>
<div style='float: left; text-align: left'>Left-aligned</div>
<div style='float: right; text-align: right'>Right-aligned</div>
</td>

If it's | Left-aligned
                                           Right Aligned |

Then Balon's solution is correct.

If it's: | Left-aligned    |   Right-Aligned |

Then it's:

<td align="left">Left-aligned</td>
<td align="right">Right-Aligned</td>

Do you mean like this?

<!-- ... --->
<td>
   this text should be left justified
   and this text should be right justified?
</td>
<!-- ... --->

If yes

<!-- ... --->
<td>
   <p style="text-align: left;">this text should be left justified</p>
   <p style="text-align: right;">and this text should be right justified?</p>
</td>
<!-- ... --->

td style is not necessary but will make it easier to see this example in browser

<table>
 <tr>
  <td style="border: 1px solid black; width: 200px;">
  <div style="width: 50%; float: left; text-align: left;">left</div>
  <div style="width: 50%; float: left; text-align: right;">right</div>
  </td>
 </tr>
</table>

You could use something like:

<td> 
  <div style="float:left;width:49%;text-align:left;">this is left</div> 
  <div style="float:right;width:49%;text-align:right;">this is right</div> 
</td>

The 49% is to give some room for the renderer to wrap things around.

And you can use either <div> or <span>