设与直线x+y=0垂直的直线方程为x-y+c=0,把点(-1,0)代入,得:-1-0+c=0,解得c=1.∴经过点(-1,0),且与直线x+y=0垂直的直线方程是x-y+1=0.故答案为:x-y+1=0.