I have been there. messed up in second year. Getting reinstated is not easy, but it is absolutely possible. In your letter you need to explain why you failed, what you learned from the experience, how you will be preventing it from happening again in the future. You also should demonstrate why you even want to be in engineering and try to prove it.
From what youve said about your case, it seems like you will be good to go. Just explain that you know you messed up and have learned not to f*ck around in the future and say it was so important to you that you even worked at a relevant company in the time you were out of the faculty.
show to them that you have genuine intentions of doing well, and have taken steps to ensure you will be successful,and they will certainly let you in
good luck with it, feel free to PM me if you need any other advice on the process. It happened to me after 2nd year as well, and it was a rough experience, so i would be glad to help.