Hello and welcome back to Justnaswer,
There is no phone number to contact the Editorial Staff at Time Magaine. The way to get to Time Magazine Editorial Staff is to contact the Editor via an E mail. This is the E mail address: firstname.lastname@example.org .
What you have to be is very professional and give them an idea of the information and article you would like to do. Be prepared as this goes to the Editorial staff and they most of the time will not accept anything from a freelace writer. If they are interested, they will respond to you via Email. You should include all contact information for yourself and any previous experience that you may have.
Good luck in your endeavor. Joan