Essentially a cease and desist letter is a request to stop an action. In your case, it is for you to stop posting "slanderous" comments about your ex.
To stop further legal action, you should first contact an attorney to review the letter and advise you as to what options you have available. You should remove the material specified in the Cease and Desist letter, which are the posts you've made on your tumblr account. You can always re-post once the matter has been settled in your favor.
If you have any questions, please contact me at email@example.com or 954-913-2273.