This example will modify the value of the selected dimension and sets its value to be equal to the equation using SOLIDWORKS API:

sin(0.5) * 2 + (10 - 5)

Equation in dimension
Equation in dimension

IEquationMgr SOLIDWORKS API interface should be used to manage equations in SOLIDWORKS document.

Dim swApp As SldWorks.SldWorks
Dim swModel As SldWorks.ModelDoc2
Dim swSelMgr As SldWorks.SelectionMgr
Dim swEqMgr As SldWorks.EquationMgr

Const EQUATION = "sin(0.5) * 2 + (10 - 5)"

Sub main()

    Set swApp = Application.SldWorks
    
    Set swModel = swApp.ActiveDoc
    
    If Not swModel Is Nothing Then
    
        Set swSelMgr = swModel.SelectionManager
        
        Dim swDispDim As SldWorks.DisplayDimension
        
        Set swDispDim = swSelMgr.GetSelectedObject6(1, -1)
                
        If Not swDispDim Is Nothing Then
                
            Set swEqMgr = swModel.GetEquationMgr
            
            Dim formula As String
            
            formula = """" & swDispDim.GetNameForSelection & """ = " & EQUATION
            
            swEqMgr.Add2 -1, formula, True
        
        Else
            MsgBox "Please select dimension"
        End If
    
    Else
        MsgBox "Please open model"
    End If
    
End Sub