tan x +x =1 ,so x=?

The question is basically flawed. What unit and domain of x?
If x is the angle in degree, tan x is a ratio, a number. You can’t add trigonometric function to an angle
tan x (a number) + x (in degree) = 1 (a number)
The question doesn’t specify the unit of angle, degrees or radians?

At any way, assuming x is measured in degrees in tan x, and
0° <= x <= 180°Solve by Newton’s method, (Calculus)
Let y = tan x +x -1
dy/dx = (sec x)^2 + 1
Xnext = Xn – function(Xn) /derivative(Xn)
Xnext = Xn – (tan x +x -1)/[(sec x)^2 + 1]

1st trial, I pick x = 0.9 because (tan x + x) is close to 1
let Xn = 0.9
Xnext = 0.9 – (tan (0.9°) + 0.9 -1)/( (sec 0.9°)^2 + 1)
Xnext = 0.9842907

2nd trial,
let Xn = 0.9842907
Xnext = 0.9842907– (tan (0.9842907°) + 0.9842907-1)/( (sec 0.98429087°)^2 + 1)
Xnext = 0.9828192

3rd trial, gives Xnext = 0.9828449. 4th trial gives Xnext = 0.9828445

If x is in degrees, the solution is: x = 0.9828445 (an approximation)

Check:
tan 0.9828445° + 0.9828445 = 1.0000000268

If x is in radians, x = 0.479731
tan 0.479731 rad + 0.479731 = 0.999999983

If you don’t specify the domain of x, there are infinite number of solutions.
Of course, you can use graphic calculator to solve it as well.

http://www.wolframalpha.com/input/?i=tan+x+%2Bx+%3D1

I don't think there is a general solution for this equation