Clean URL with url parameters

Hi all,

I have a website and I want to expand it with a product catalogus (category and productdetail pages). I’ve build it with php and when a visitor clicks on a product in the category view, a few parameters passes through the url. So for example I have:

Category page (www.domain.com/washingmachine)
–miele w3203
–bosch 232323
–aeg zzaadd21
–etc

And when a visitor click on the miele w3203 the url is:
https://www.domain.com/detail?cat=wasmachingmachine&idnummer=658

The productdetail page is a seperate template page. This works, only the url is very bad. I want to like this:
https://www.domain.com/washingmachine/miele-w3203

I use a custom MySQL query on the productdetail page where I need the category and id of the clicked product.

global $wpdb;
$databasetabel =  $_GET['cat'];
$idnummer = $_GET['idnummer'];

	$data = $wpdb->get_results("
		SELECT *
		FROM  $databasetabel
		WHERE idnummer=".$idnummer."
		LIMIT 0, 100;
	");

I really want to use the WordPress add_query_vars but I’ve tried all day and I can’t figure it out. How can I get the url I want and what is best practice here? How can I pass parameters from a category page to a detailpage without placing them in the url? Or do I need a rewrite? Really confused here!

Thanks so much for helping me out!!!

Kind regards,
Mark