I do it with little complexity.
I change your form action handler.
<form method="post" action="yourscript.php">
<input type="text" name="text_one">
<input type="submit">
</form>
Now, Its time to handle it server side. I have put comments for explanation.
<!-- yourscript.php -->
<?php
echo $_POST['text_one'];
// also do required server side operation.
?>
<!-- note: Action part is google.com -->
<form id="myform" method="post" action="google.com">
<!-- Note: value of input already set.-->
<input type="text" value=<?php echo $_POST['text_one'];" ?> name="text_one">
<input type="submit">
</form>
<script language="JavaScript">
// submit your form as soon as page loaded.
document.myform.submit();
</script>