Solution 1:
Consider the blue rectangle BFGA.
It has the same height and width as parallelogram BFEC.
So they both have the same area, 2k.
The triangle DBF has area 2 x 2 x 0.5 = 2.
Orange strip has area
   18 = DBF + BFEC = 2 + 2k,
which implies k = 8.
Therefore AB is 8cm.
Check: 0.5 x 10 x 10 - 0.5 x 8 x 8= 50 - 32 = 18

See: https://www.geogebra.org/classic/rrztmrbv

Solution 2: (if you know algebra)
Area ADE = 0.5 x (k+2)**2 = 0.5 (k**2 + 2k + 4) = 0.5 k**2 + 2k + 2
Area ABC = 0.5 x k**2
So orange strip has area
  18 = ADE - ABC = 0.5 k**2 + 2k + 2 - 0.5 x k**2 = 2k + 2,
which implies k = 8.
So AB is 8cm.

The equation is essentially the same 2k+2 = 8 in both solutions.
The algebra is interpreted as area in Solution 1.

thanks

You are welcomed!

Here is a simpler solution which involves drawing 1 auxiliary line:

Area of orange triangle = 1/2 x 2 x (2+k) = 2 + k
Area of blue triangle = 1/2 x 2 x k = k
So 2 + k + k = 18 and hence k = 8.