MAIL + C = CLAIM
EXIT + S = EXIST
GOSH + T = GHOST
CITY + H = ITCHY
NEWT + I = TWINE
DENY + E = NEEDY
MINI + M = MINIM
And the letters CSTHIEM spell CHEMIST.
Your objective is to place some diagonal 'mirrors' into the grid.
If a ray of light is shone in to the grid from each of the letters, and allowed to bounce off the internal diagonal mirrors, each will exit the grid at the twin of the letter that it entered the grid. For example, a ray entering at either letter D will bounce off some mirrors and exit the grid at the other letter D.
Each row and each column will contain exactly two of the diagonal mirrors.
Fill in the missing numbers with the digits 1 to 9. A diamond shape in the middle means that the four numbers around it add to 20.
Each uses a different way to add to 20, i.e. if there is already 1 + 3 + 8 + 9, then there will not be another using the digits 1, 3, 8 and 9 (in any order). The same digit isn't allowed to touch, even diagonally.