Inverting the encryption equation of a symmetric cipher I've just started a cryptography course. I am beginning to understand the concepts (I'm only in week 2) but I just can't get my head around the theories and principles when written as equations.

I've been posed the below question to answer:


  Consider a very simple symmetric block encryption algorithm in which 64-bit blocks of plaintext are encrypted using a 128-bit key. Encryption is defined as:
  
  $$C = (P ⊕ K_0) ⊞ K_1$$ 
  
  Show the decryption equation, that is, show the equation for $P$ as a function of $C$, $K_0$ and $K_1$
  
  
  $C$ = ciphertext
  $P$ = plaintext
  $K$ = secret key
  $K₀$ = leftmost 64 bits of secret key
  $K₁$ = rightmore 64 bits of secret key
  $⊕$ = bitwise exclusive or (XOR)
  $⊞$ = addition mod $2^{64}$
  


I simply don't understand what the function of $⊞$ serves. 

Can anybody assist me with tackling this problem? I just don't know where to start other than to $P = (C.....)$ possibly? I'm unsure as to what the 'addition mod 2⁶⁴' refers too.

EDITED FOR CLARIFICATION

So if for example, our plaintext is:-

messagea (ASCII)

01101101 01100101 01110011 01110011 01100001 01100111 01100101 01100001   (binary - 64 bit)

and our 128-bit secret key is:-

mysecretpassword (ASCII)

01101101 01111001 01110011 01100101 01100011 01110010 01100101 01110100 01110000 01100001 01110011 01110011 01110111 01101111 01110010 01100100 (binary - 128 bit)

To achieve the first past of the algorithm, "C=(P⊕K₀)", I XOR the plaintext against the first 8 characters (64 bits) of the secret key to get the following:-

01101101 01100101 01110011 01110011 01100001 01100111 01100101 01100001 

01101101 01111001 01110011 01100101 01100011 01110010 01100101 01110100 ⊕



00000000 00011100 00000000 00010110 00000010 00010101 00000000 00010101

Now, how do I then apply '⊞K₁' to the above? I am aware that I need to do something with the above to the last 64-bits of the key but I'm unsure what calculation. If someone could walk me through it, that'd be great. Thanks
Addition modulo $N$ in the above example is another way of key mixing that adds more non-linearity to the cipher as it operates across a group of $N$ bits, vs XOR which is addition modulo 2 on individual bits. For example, where $N=2^6$ or 64:

$44 ⊞ 44 = 24$

$44 ⊕ 44 = 0$

Addition within larger groups is also used in mixing operations such as Pseudo Hadamard Transformations. Key addition instead of XOR also plays a prominent role in the block ciphers Twofish and IDEA.

Edit:
Here are posts with more detail on the choice of addition:

What exactly is addition modulo $2^{32}$ in cryptography?

Why Addition Mod 32?