Well, you could do it with a black powder motor if you calculate the burn time such that during the landing phase the TWR of the entire rocket dips below 1 unti

Well, you could do it with a black powder motor if you calculate the burn time such that during the landing phase the TWR of the entire rocket dips below 1 until a descent velocity is achieved and then stays at 1 until landing where you need a bit over 1. TL;DR extremely (impossibly) hard but not completely impossible if you solve the above problem. You need atleast a hybrid motor IMO, something where you can control the thrust atleast partially (below and above 1 TWR). Whether or not you use the same motor for landing or takeoff is another question, you can use the same motor for both if it has enough fuel and TWR.