I managed to solve it using onChange="javascript"
This solution will help in the situation where....the user clicks on the option(ID), and it will show the corresponding (NAME) in the textbox in the same page.
include('connect2db.php');
$query = "SELECT employee.Emp_ID, employee.Emp_Name FROM employee,supervisor WHERE employee.Supervisor_ID = supervisor.Supervisor_ID AND supervisor.Supervisor_ID = '".$_SESSION['EmpID']."' ORDER BY employee.Emp_ID;";
$result = mysql_query($query);
echo '<select name="emID" onChange="javascript:EName.value = emID.options[emID.selectedIndex].value;" id="emID" style="width: 100px;">';
while($row = mysql_fetch_array($result,MYSQL_NUM)){
echo '<option value="'.$row[1].'">'.$row[0].'</option>';
}
echo '</select>';
echo '<input type="text" style="width: 250px; name="EName" id="EName" ></input>';