I use http://github.com/abraham/twitteroauth PHP library for reaching the Twitter REST API. My config file has credentials:
<?php
$consumer_key = 'xxxxxxxxxxxxx';
$consumer_secret = 'xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx';
$login = 'xxx';
$passwd = 'xxx';
?>
Is it possible to get oauth_token and oauth_token_secret without showing the Twitter login page?

As the comments state, you can’t do this. Once the you have authorised, you can then store the returns and use them in all your calls, keeping your connection “persistant”