Use Nodal Analysis to determine V₁ and V₂.

The original circuit is shown in black. The RED items were added.

Note that if the bottom node is chosen as the reference node, the remaining two essential node voltages are V₁ and V₂, thus I have labeled them as such.

V₄ was added to help calculate the current out of node 1 through the 4 W resistor.

I will sum the currents OUT OF the nodes.

First, I will determine V₄ from KVL.

V₁ = V₄ + 144

so

V₄ = V₁ - 144

Now, write KCL at node 1 and 2

Node 1:

(Eq. 1)

Node 2:

(Eq. 2)

Solving the two equations yields

V₁ = 100 V

V₂ = 20 V