Extract Every Instance of Entry to Another Sheet

You'll see this much better in the sample sheet. I wish to do the following:

In sheet "ThisWeek", I want to look up each entry of Column T (Horse) in sheet "ALL". I then want copy EVERY instance (and the entire row of data) of that entry into sheet "Extracted." Now, I gave just a smattering of the info. The real sheets go up to column JF. I'm not sure that matters. And yes the sheets have a header so the search/paste will have to begin at A2. Also, I want the data to pile up of course and not overwrite. Meaning, I could have a list of 100 horses that could return over 1000 matches. I want that list of over 1000 to appear in the Extracted sheet. I hope explained this clearly. I'm tired. Please help!