Add custom query vars to pretty permalinks

Use add_rewrite_rule to capture the url and convert to params internally.

http://example.com/page{p}/t/{t}

to 

http://example.com/?p={p}&t={t}

Add to your function.php or in a plugin.

<?php

if ( ! class_exists( 'SimpleRewrite' ) ):

    class SimpleRewrite {
        const ENDPOINT_QUERY_NAME  = 'page';
        const ENDPOINT_QUERY_PARAM = '__rewrite_page';

        // WordPress hooks

        public function init() {
            add_filter( 'query_vars', array ( $this, 'add_query_vars' ), 0 );
            add_action( 'parse_request', array ( $this, 'sniff_requests' ), 0 );
            add_action( 'init', array ( $this, 'add_endpoint' ), 0 );
        }

        // Add public query vars

        public function add_query_vars( $vars ) {

            // add all the things we know we'll use

            $vars[] = static::ENDPOINT_QUERY_PARAM;
            $vars[] = 'p';
            $vars[] = 't';

            return $vars;
        }

        // Add API Endpoint

        public function add_endpoint() {
            add_rewrite_rule( '^' . static::ENDPOINT_QUERY_NAME . '([^/]*)/t/([^/]*)/?', 'index.php?' . static::ENDPOINT_QUERY_PARAM . '=1&p=$matches[1]&t=$matches[2]', 'top' );

            //////////////////////////////////
            flush_rewrite_rules( false ); //// <---------- REMOVE THIS WHEN DONE
            //////////////////////////////////
        }

        // Sniff Requests

        public function sniff_requests( $wp_query ) {
            global $wp;

            if ( isset(
                $wp->query_vars[ static::ENDPOINT_QUERY_PARAM ],
                $wp->query_vars[ 'p' ],
                $wp->query_vars[ 't' ] ) ) {
                $this->handle_request(); // handle it
            }
        }

        // Handle Requests

        protected function handle_request() {
            global $wp;

            $page = $wp->query_vars[ 'p' ];
            $t    = $wp->query_vars[ 't' ];

            add_filter( 'template_include', function( $original_template ) {
                return __DIR__ . '/custom.php';
            } );
        }
    }

    $wpSimpleRewrite = new SimpleRewrite();
    $wpSimpleRewrite->init();

endif; // SimpleRewrite

To limit params to only numbers “\d” change the rewrite match to:

'^' . static::ENDPOINT_QUERY_NAME . '(\d*)/t/(\d*)/?'