You can use hidden field like this

<form action="" method="post">
      <input type="hidden" name="new_value" value="value"/>
      <input type="text" value="" size="30" name="email" id="email">
      <input type="submit" name="submit" value="Submit" class="continue-button">
</form>

or you can add to action of form like this

<form action="http://action_url?new_value=value" method="post">
      <input type="text" value="" size="30" name="email" id="email">
      <input type="submit" name="submit" value="Submit" class="continue-button">
</form>