To solve for the current values, we can use Ohm's Law and Kirchhoff's Voltage Law (KVL).

First, let's calculate the total resistance (Rt) in the circuit:
Rt = R1 + R2 = 10Ω + 5Ω = 15Ω

Now, we can use Ohm's Law to calculate the total current in the circuit (It):
It = S/Rt = 10V / 15Ω = 0.67 A

Next, we can use KVL to find the current through each resistor:
V = IR
For Loop 1 (R1):
10V = I1 * 10Ω
I1 = 10V / 10Ω = 1 A

For Loop 2 (R2):
10V = I2 * 5Ω
I2 = 10V / 5Ω = 2 A

Therefore, the current through R1 (I1) is 1 A and the current through R2 (I2) is 2 A.