How does this affine cipher work? I have a question about how I need to solve the following:

A sentence has been changed to ASCII and then encrypted with the formula $E(x) = ax + b \bmod 256256$. All I know is that the first 4 letters are: W I S K

This is the encrypted message:

 064066 158368 092525 143358 099354 141643 110102 051667 024006 190286 133343


How do I go about solving this? I first tried to program a brute force but I actually want to understand how to solve it. I tried working with the extended euclidean algorithm as well, but didn't get far.
W is 87 in ASCII, so
$$
87a+b\equiv064066\pmod{256256}.
$$

I is 73 in ASCII, so
$$
73a+b\equiv158368\pmod{256256}.
$$

Subtracting, you get
$$
14a\equiv-94302\equiv161954\pmod{256256}.
$$

Unfortunately 14 is not coprime to 256256, so you'll need to use other letters to figure this out. Once you get an equation of the form
$$
ma\equiv n\pmod{256256}
$$
you can solve for $a\pmod{256256}$ and then substitute to find $b\pmod{256256}.$

(In fact, you already have enough to solve with trial and error, but it's nicer to avoid that.)