If you have no option to use server-side programming, such as PHP, you could use the query string, or GET parameters.
In the form, add a method="GET"
<form action="display.html" method="GET">
<input type=""text"" name=""serialNumber"" />
<input type=""submit"" value=""Submit"" />
</form>
When they submit this form, the user will be directed to an address which includes the serialNumber value as a parameter. Something like:
http://www.example.com/display.html?serialNumber=XYZ
You should then be able to parse the query string - which will contain the serialNumber parameter value - from JavaScript, using the window.location.search value:
// from display.html
document.getElementById("write").innerHTML = window.location.search; // you will have to parse // the query string to extract the // parameter you need