Let us think about the possible minimum value of "g(n) - h(n)" ..
Let g(n) = 2n
h(n) = 2n ..Both are valid functions as 2n = O(n) = Ω(n)
Now g(n) - h(n) = 2n - 2n = 0 [means a constant]
Means minimum value of g(n) - h(n) may be a constant as well..
Hence in that case f(n) will be dominating as f(n) = θ(n) ...
Now let g(n) = n3 h(n) = n
Hence g(n) - h(n) = n3 - n which is asymptotically larger than n..Hence in this case "g(n) - h(n)" will dominate over f(n) ..
So we see in any case we wont get less than order than n..In the first case due to first term we are getting a function of n and in the second case larger than function of n..
Hence lower bound is function of n..
Hence f(n) + g(n) - h(n) = Ω(n)