Using the Loop rule to find potential Difference

[MasterVivi]

Homework Statement

Find the potential difference between points a and b.

Picture of Circuit involved.

Homework Equations

V=IR
ΔV=V_b-V_a

The Attempt at a Solution

Pretty much completely lost, due to the only one current shown I'm not sure which way the current flows through the rest of the circuit so I do not know how to go about the loop rule.
It started off kinda like

-I₁(30Ω)=2.118 V

But I know that cannot be correct cause if you left from the 24V battery and went down you'd have something about 23.3V across there, like I said, completely lost, any help would be great.

 

[Spinnor]

If you study some worked out examples you might figure out the rules?

See,

http://commons.bcit.ca/math/examples/elex/linear_algebra/backgd4.html

Found here,

https://www.google.com/search?hl=en..._gc.r_pw.r_qf.&cad=b&sei=MwB6UKSSE-K40gGR-oBQ

 

[MasterVivi]

This is useful, in a case like mine you wouldn't want multiple I notations of current cause then your introducing variables you don't know right?
should I go opposite the current from b→a?
like
ΔV=-(0.0706A)(10Ω)+12V=12.706V

Since that is the only value of I given?

 

[MasterVivi]

Using the one know current, the current would be the same at a correct?
If so you couls just do
V_a-V_b=-24V+(I)(10)
=>-24+(0.0706)(10)=-23.294

Which implies
V_b-V_a=+23.294V

Or is this still the wrong path?
Do I need to use loop rules and find the unknown values of the current when it splits?