To simplify this expression, we will first calculate the values of the exponents and then perform the operations.

2.6^9 = 2.6 * 2.6 * 2.6 * 2.6 * 2.6 * 2.6 * 2.6 * 2.6 * 2.6 ≈ 1,018.992

2^5.18 = 2 * 2 * 2 * 2 * 2 * (approximately) 35.938

2.6^4 = 2.6 * 2.6 * 2.6 * 2.6 ≈ 45.496

2^2.6^8 = 2 * (approximately) 1,018.992 ≈ 2,037.984

Now, let's substitute these values back into the expression:

1,018.992 - 35.938 * 45.496 / 2,037.984

Next, we will perform the multiplication and division:

1,018.992 - 1,635.414 / 2,037.984

Now, we will perform the division:

1,018.992 - 0.803

Finally, we will perform the subtraction:

1,018.189

Therefore, the simplified expression is 1,018.189.