How many liters of water should be added to 18 liters of 14% bleach solution so that the remaining solutions contains only 10% bleach

We must take that the 14 % is volumentric. This is we will use only volumetric measures.

From the original solution you can find the quantity of bleach.

Original solution: 18 liters * [14 liters of bleach / 100 liters of solution] = 2.52 liters.

Now you know that those 2.52 liters shall represent the 10% of the new solution, after having added x liters of water. Then:

[2.52 liters of bleach]  / [volume of solution] = 10% = 0.1

=> volume of solution =   2.52 liters  / 0.1 = 25.2 liters of solution.

That tells you that you have to add 25.2 liters - 18 liters =   7.2 liters of water.

Check that in that case you will have:

2.52 liters of bleach

18 liters of the original solution

7.2 liters of new water added to the original solution.

2.52 liters of bleach / [18 + 7.2] liters of solution = 0.1 = 10%.

Then, the answer is: 7.2 liters of water should be added.