The dual-arm manipulation of elastic wires has been a hard problem for many decades. Nevertheless, recent work has shown that the shape of a wire can be defined by a very simple representation. Theoretical analysis has stated that simple sensing of the force and torque at one end of the wire can be used to determine its shape. In this letter, we experimentally analyze the developed theoretical foundation. We deploy a dual-arm robotic system able to accurately manipulate an elastic wire. The system does not require complex visual perception and is able to reason about the shape of the wire by solely sensing forces and torques on one arm. Furthermore, we propose a full framework in which the mechanical properties of the wire are rapidly approximated in real-time. Then, a simple control rule based on Force/Torque feedback is used to manipulate the wire to some goal or track a planned path. We conduct various experiments on a full-scale system to analyze pose estimation and control accuracies. Results validate the benefit of the approach and demonstrate the ability to accurately manipulate a wire.