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>