The left schematic combines \$R_1\$ and \$R_2\$. The right schematic eliminates \$R_3\$ since it has no impact on the current source (which has infinite impedance.)

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![schematic](https://i.sstatic.net/RGLGt.png)

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At this point, it's convenient to Nortonize the Thevenin source presented by \$E\$ and \$R_1+R_2\$ and then follow through with some steps, as shown below:

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![schematic](https://i.sstatic.net/95WAq.png)

<!-- End schematic -->

At this point, you should already know that the maximum power into \$R_\text{LOAD}\$ will occur when \$R_\text{LOAD}=R_\text{TOTAL}\$. (If not, you can compute this by developing a power equation and then solving for the derivative, where the slope is zero.)

The voltage at the load resistor will be exactly \$\frac12\$ of the applied voltage shown above. Given that you know that \$R_\text{LOAD}=R_\text{TOTAL}\$, you should now be able to easily work out the power in \$R_\text{LOAD}\$.


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Here's a curve generated using Spice to show the power in \$R_\text{LOAD}\$ as it's resistance is varied. You should expect to see something akin to a parabolic curve. And you do:

[![enter image description here][1]][1]

You can also see that the estimated resistance I'd calculated is consistent with the graph.


  [1]: https://i.sstatic.net/ZGbsH.png