Possible to find the operator $A$ if I know the operators $K$ and $B$ and the spectrums are related by $\sigma(K) = \sigma(A) \bigcup \sigma(B)$?

Question

Suppose I have a bounded linear operator $K$. Let's say the spectrum of $K$ is the union of the spectrum of two other operators, that is

$$\sigma(K) = \sigma(A) \bigcup \sigma(B)$$

Now if I know the operator $B$ is it possible to find the operator $A$?