Given the power absorbed by each resistor, and the resistance value – do I have enough information to solve the circuit?
I found the Voltage Supply value by \$v^2=pr\$ but I'm not sure how to find the currents for \$V_{in}\$, or the branch currents…
I created 4 mesh equations – the three along the bottom, and one along the edge . but since I dont know \$V_{in}\$ I can't create my matrix to solve for \$V_{k}\$.
EDIT:
I am very aware of \$p=iv\$ and \$v=ir\$
I am able to find individual Voltages and Currents but not what the values of \$V_{in}\$ and \$I_{in}\$ are. I'm not sure how to tell what the direction of these currents are. I'm trying to find out if the \$I_{in}\$ absorbing or delivering power – to dot that, do I need to know the directions? To find \$V_{in}\$ can I sum the individual currents? \$v=\sqrt{p_{1} r_{1} + p_{2} r_{2} \cdots p_{n} r_{n}}\$. What do I do with the current source?
from here: 
Best Answer
Using the mesh or node equations, you should be able to determine each of the currents and voltages in the circuit in terms of \$V_{in}\$ and \$I_{in}\$. This will give you 10 equations of the form
$$V_j = f_j\left(V_{in},I_{in}\right)$$ and $$I_k = g_k\left(V_{in},I_{in}\right)$$
Now you say you are given the power consumed by each resistor, which means a set of equations of the form
$$V_nI_n=P_n$$
where the \$P_n\$ are known values.
This will be more than enough equations to be able to determine \$V_{in}\$ and \$I_{in}\$. All you need to do is pick the most convenient couple of equations and do some algebra.