How to show Wordpress blog posts in Drupal's Search Api?
There are 2 ways you can achive this :


[simple] Import the posts from wordpress rss with Feeds https://www.drupal.org/project/feeds
[more difficult] Crawl the Wordpress content and populate the Apache Solr index directly. You can use an open source crawler like Apache Nutch
The difficult part is that the external content is not managed by Drupal, only through Solr so you don't have many options to play with the indexed content in the Drupal site.